Rory McIlroy through at WGC-Dell Match Play

McIlroy was two down after 13 holes against Thorbjorn Olesen at Austin Country Club, but saw the Dane bogey three of the last five holes, including a shanked chip shot on the 18th.

“I do feel fortunate,” McIlroy admitted. “I was not up until the final hole and feel a little bit bad for Thorbjorn. He played pretty solid and just had a bad finish and opened the door for me.

“After I went two down after 13 a switch sort of flipped on for me and I started to hit some quality shots. I was a little flat for the front nine but coming in I started to hit some good quality shots and I am happy with that.”

Day had earlier headed straight into the clubhouse for treatment after injuring his lower back in the closing stages of his 3&2 victory over Graeme McDowell in their group match.

The 28-year-old, who recovered from two down after four holes, did not speak to reporters but his coach and caddie Colin Swatton said he first noticed an issue on the 15th tee.

“He grabbed his back and said, ‘Oh, I just tweaked it,’” Swatton said in quotes reported by GolfChannel.com. “Up until that point, there was nothing.

“He’s been great all year. Just out of the blue. I don’t know if it was one swing or what it was.”

Day also grimaced and immediately let go of the club after pulling his tee shot on the 16th and had to back gingerly into a fairway bunker before playing his second shot.

“I’m not going to say it rubbed salt in my wound when a guy is three up with three to go and then he starts hurting and is able to limp up and win the match, but it does put a salty edge in it for me,” McDowell joked. “Go down six holes ago if you’re going.”

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

World number one and Texas native Jordan Spieth beat 2014 Ryder Cup hero Jamie Donaldson 3&2, but insisted his local knowledge was not a huge advantage this week.

“We came here maybe once a week,” the Masters and US Open champion said. “It’s certainly a slight advantage but there have been significant changes, especially in the green complexes.”

The biggest win of the opening day saw Matt Kuchar thrash Anirban Lahiri 6&5, while Phil Mickelson did not lose a single hole in beating England’s Matt Fitzpatrick 5&4.

Belgium’s Thomas Pieters, who was dressed all in black in tribute to the victims of the terrorist attacks in Brussels, halved his match with Adam Scott thanks to birdies on the 16th and 17th, while Jason Dufner did the same to edge out Rickie Fowler 2&1.

Former Ryder Cup team-mates Sergio Garcia and Lee Westwood endured a rollercoaster contest which saw just three holes halved before Garcia emerged victorious on the 18th.

Garcia was two up after three before losing the next four holes in succession, only to then win four holes in a row himself from the ninth to gain some semblance of control.

“It was very, very funny,” Garcia told Sky Sports. “Lee said to me on 17, ‘We are gelling well!’ It would have been better in a fourball.

“It was very up and down. I started very well and he hit a couple of poor shots, then he got on a great run and the last three or four holes he was making birdie or I was. I’m very happy with the putt I made on 18 to get the win.”

Twelve of the 32 matches went to the 18th hole, with Justin Rose almost letting slip a four-hole lead before defeating Argentina’s Fabian Gomez while two-time major winner Martin Kaymer edged out Ireland’s Shane Lowry.

Danny Willett halved his match with South Africa’s Jaco van Zyl, while Scotland’s Russell Knox had to settle for half a point against Sweden’s David Lingmerth.