Rory McIlroy got lucky at the death but Shane Lowry and Graeme McDowell both ended up with defeats on the first day of the WGC-Dell Match Play in windy Austin.

The world No 3 was two down with five to play in a scrappy match with Thorbjorn Olesen but he found something under pressure and took advantage of mistakes by the Dane to win the 18th with a par and steal a one up win that felt like daylight robbery.

“You feel bad because he's up basically the whole match, and to finish like that, as well," McIlroy generously conceded. "If I had birdied 18 and he parred it, I would feel like I won the match and he probably would feel the same way.

"Whereas he's definitely going away like he lost it. It was his to lose. I feel a little bit bad for him, but I'm just happy that I snuck through with the win and I’m looking forward to the next couple of days.”

If it was a frustrating day for Olesen, it was infuriating for Lowry, who had a seven footer to go two up at the 15th but then lost the 16th to a brilliant Martin Kaymer birdie, three putted the 17th to go one down and shook hands on the last as the German drove the green and putted up close to match his birdie.

McDowell fell by 3 and 2 to Jason Day, who hobbled off the course complaining of back pain just two weeks before the Masters where he was expected to be one of the favourites.

As Thongchai Jaidee beat Paul Casey 2 and 1 in the other Group 2 clash, it remains to be seen how well Day recovers so that he can face the Thai today after he limped away and had treatment from not one but two physios.

“Jason tweaked his back on hole No. 15 and had some work done post round,” Bud Martin, Day’s agent, said in a statement. “He is pleased with the outcome of the match and is getting prepared to play tomorrow.” 

Having won the Arnold Palmer Invitational at Bay Hill on Sunday and with two Top-3 Masters finishes since 2011, many see 28-year old Day as one of the clear Masters favourites.

But his latest health scare — he was severely hampered by vertigo in last year’s US Open and has twice suffered back problems at events in recent years — casts a shadow over what looked like a perfectly timed run to Augusta National.

McDowell will feel he let Day off the hook on a course that suits him game.

He holed from five feet for birdie on the third and was conceded the fourth after Day found trouble off the tee to go two up.

But Day didn’t go away and his power was key as he hit a 356 yard drive to the edge of the fifth green and two putted for birdie to reduce the deficit to one hole

He then birdied the sixth, eighth and ninth to turn one up and doubled his advantage at the par-three 11th where McDowell hit his tee shot into the water and conceded.

He appeared to be cruising to an easy win when he birdied the par-five 12th from 12 feet to go three up but experienced shooting pain in his lower back and legs after his tee shot at the 15th, where he holed a clutch 11 footer for par to remain three up.

He then cried out in pain and dropped his driver on the 16th tee but struggled on to win the match with a half in par fives.

McIlroy’s match was a poor quality affair that Olesen threw away with some poor putting and dubious decisions at the death.

In fairness to McIlroy, he put his game face on and hit some good shots coming down the stretch having hit pulls into water at the 12th and 13th to find himself two down.

The latter cost him a hole, and while he explained that his two iron rode the wind he was trying to use to get close to the green, he has struggled a few times with pulls and hooks over the past two weeks.

“Scrappy,” McIlroy said of a match that he squared with a par at the 14th and a birdie three at the 15th, where Olesen overshot the green and failed to give himself a putt for par. 

“The quality of golf out there wasn't too good. I feel like it's hard for the quality to be that good too because the wind is gusty.”

After a halves in pars at the 16th and 17th, McIlroy drove into a green side trap short of the 18th and watched as Olesen hit a fairway metal left into the rough, overshot the green again with his second and took three more to get down.

“I didn't have my best stuff today, but I hung in there and hit good shots when you needed to. I felt like I played tee to green very well from sort of 14 on. So I'm just happy to get the win.

“It was a day where you just sort of had to hang in there. With the wind it's tricky. It swirls around here. It drops, it gusts. It's tough to pick a club. I really struggled with that today. I hit some good shots, but I just had to grind out pars and that's what I did coming in and ultimately that was good enough.

“I know if I want to progress further in this tournament, I'm going to have to play better than I did today.”

Asked if he upped the intensity level after going two down with five to play, he said: “I sort of needed that. I felt like the first few holes I was a little bit flat. I think teeing all off so late as well, I came off at 2:20. We're not really used to do doing that too much. I was a little flat the first few holes. Once I needed to play well, I felt like I went up a gear and hit some good shots on the way.

“Match play is all about just getting through. Especially this time you don't have to play your best golf these rounds. You have to get through and get by and get into the weekend. I'm one step towards doing that after today. I know that I'm going to have to play a bit better if I want to win my next matches.”

On his experience of dealing with pressure down the stretch, he said: “I draw upon it a lot. I know that when I need some of that stuff, I'm able to produce it. So that's huge. I'm going to have to do that more and more as the week goes on, because the matches only get tougher. The quality of my play needs to get better, as well. But the way I played the last five holes, if I can continue that, I'll be happy.”

As for the new Nike two-iron he put in the bag, he explained: “It goes miles. It goes so far. It's a great club in the wind, the ball flight is really, really stable. I tested it with Nike a couple of weeks ago and thought it would be perfect for the likes of Oakmont and Troon.

“But getting here this week and seeing the golf course, it's sort of great for here as well. The ball speed I'm getting off it is close to some guys' drivers. Flight probably carries 265, 270 and runs close to 290. So it's hopefully going to be a great club this week, but I think for the summer coming up, some of the golf courses it's going to be a great club.

McIlroy will next play Smylie Kaufman who lost 2 and 1 to Kevin Na in their Group 3 game.

In Group 14, Lowry will be looking for a win Marcus Fraser, who fell to an impressive Zach Johnson by 4 and 3.

Kaymer will take on Johnson and he’ll be looking for a repeat of some of the clutch shots he pulled out of nowhere to rattle Lowry.

“It was a sensational finish, but the rest was very average, I would say. I didn't hit many fairways today. I couldn't really get the driver going, but I stayed into the game,” Kaymer said. “We gave each other way too many chances. 

“Both of us had chances to really close the match on 14 and 15. Shane had a huge putt on 15 to go 2-up. Then possibly I made a great birdie on 16. So very pleased with the finish.”

On the thrill of winning a pressure match, just as he did in the 2012 Ryder Cup at Medinah, Kaymer said: “It’s difficult to describe how much I love that pressure, because you don't get it anywhere else. You get it when you try to win tournaments. 

“When you are in contention after nine holes, you have to feel it. In match play it can come up every single day and that is such a beauty. You can't practice it and you need to adjust in the situation.

McIlroy didn’t play well but emerged stronger from day one, as did Jordan Spieth, who beat Welshman Jamie Donaldson 3 and 2.

No 4 seed Bubba Watson lost the 18th to a birdie to halve with No 63 seed Patton Kizzire 

while No 5 seed Rickie Fowler lost to Jason Dufner 2 and 1.

Adam Scott was also held to a halved match by Belgium’s Thomas Pieters and like the rest of the field, both wore ribbons a mark of respect for the victims of the terrorist bombings in Brussels.

As for Phil Mickelson, he also showed he’s close to his best form with a 5 and 4 thrashing of Matthew Fitzpatrick while Sergio Garcia beat Ryder Cup team mate Lee Westwood one up in a match featuring just three halves.