McIlroy was gifted an opening victory on the 18th hole against Thorbjorn Olesen in the WGC-Dell Match Play on Wednesday.
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 on Sky Sports.
"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."
Former champion Jason Day recovered from an early deficit to beat Graeme McDowell 3&2 in their group match .
But the world number two then headed straight into the clubhouse for treatment after appearing to injure his lower back while hitting his tee shot on the 16th hole at Austin Country Club.
McDowell holed from five feet for birdie on the third and was conceded the fourth after Day found trouble off the tee, but the Australian hit back by driving the green on the par-four fifth to set up a winning birdie.
Further birdies on the eighth and ninth took the US PGA champion into the lead and he doubled his advantage on the 11th when the Ulstermanl, who won the Volvo World Match Play in 2013, found water off the tee.
Day also birdied the 12th to move three up and pars thereafter were enough to seal victory, but the 28-year-old looked in considerable discomfort following his tee shot on the 16th and had to climb gingerly into a fairway bunker to hit his second shot.
There was also an opening defeat for Shane Lowry as he lost out to Germany's Martin Kaymer, 1up.
The Offalyman was one ahead with three to play, but then lost the par-5 16th and then three-putted for a bogey on 17. Both players then birdied the last.
Elsewhere, Thailand's Thongchai Jaidee defeated England's Paul Casey 2&1, while there were also narrow victories for Charl Schwartzel over Danny Lee and Brandt Snedeker against Charley Hoffman.
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.
