McIlroy backed up a 5&4 victory over American Luke List in his opening match at Austin Country Club with a 3&2 success against South African Justin Harding to put himself on the verge of a spot in the last 16.
The four-time major champion, who won The Players Championship at Sawgrass just under a fortnight ago, will progress to the knockout phase if he avoids defeat to Englishman Matt Fitzpatrick in his final group game.
“I feel good,” McIlroy, who was all square with Harding with seven to play before making an eagle at the 12th then birdied the 15th before closing the match out with another eagle-3 at the 16th, told Sky Sports. “If anything, I played better today than yesterday. Justin put up a really good fight. I had to play well. I had to make a few birdies to hang in on the front nine. Then to finish way I did was very nice.”
Molinari raced to the turn in 30 as beat Dane Thorbjorn Olesen 4&3 to claim a seventh match-play victory in a row after his heroics in last year’s Ryder Cup in France. He will also progress by avoiding defeat to former US Open champion Webb Simpson.
Stenson, who has committed to the ASI Scottish Open in July, faces Jim Furyk in a group decider after they beat Jason Day and Phil Mickelson respectively in the event’s “Group of Death”.
Furyk’s second success has almost certainly secured him a spot in The Masters with a move into the world’s top 50 at the final cut-off on Monday.
Justin Rose, the world No 2, made three birdies in the last four holes to earn a halve with fellow Englishman Eddie Pepperell, a result that keeps him in control of his own destiny.
However, three-time champion Tiger Woods will need other results to go his way in the final group games to advance after losing 2&1 to Brandt Snedeker.
Dunhill Links champion Lucas Bjerregaard holds the outright lead in his group, as do Branden Grace, Matt Kuchar and Haotong Li Haotong, who three-time major winner Brooks Koepka.
Russell Knox lost for the second day running as he went down by two holes to Australian Marc Leishman, meaning the Scot is out of the running for a place in the knock-out phase.
Knox, who needed to reach the semi-finals on Sunday to get into The Masters, had his nose in front early on before Leishman won the fifth and seventh, where he rolled in a long birdie putt.
A monster 425-yard drive helped Leishman go two up with an eagle-3 at the 12th and, though Knox kept fighting, it just wasn’t to be for the second day running after he’d lost in similar circumstances to Bryson DeChambeau on Wednesday.
“Playing very solid and under par both rounds,” he wrote on Twitter. “Only one bogey a day, but guess not enough birdies.”
Full second-day results
Paul Casey (Eng) halved with Charles Howell III (US)
Cameron Smith (Aus) lost to Abraham Ancer (Mex) 3&2
Francesco Molinari (Ita) bt Thorbjorn Olesen (Den) 4&3
Webb Simpson (US) halved with Satoshi Kodaira (Jpn)
Bubba Watson (US) lost to Billy Horschel (US) 2&1
Jordan Spieth (US) bt Kevin Na (US) 3&2
Justin Rose (Eng) halved with Eddie Pepperell (Eng)
Gary Woodland (US) bt Emiliano Grillo (Arg) one hole
Jason Day (Aus) lost to Henrik Stenson (Swe) 4&3
Phil Mickelson (US) lost to Jim Furyk (US) one hole
Justin Thomas (US) bt Matt Wallace (Eng) 3&1
Keegan Bradley (US) halved with Lucas Bjerregaard (Den)
Tiger Woods (US) lost to Brandt Snedeker (US) 2&1
Patrick Cantlay (US) bt Aaron Wise (US) 4&2
Rory McIlroy (NIrl) bt Justin Harding (Rsa) 3&2
Matthew Fitzpatrick (Eng) lost to Luke List (US) 2&1
Xander Schauffele (US) halved with Tyrrell Hatton (Eng)
Rafael Cabrera-Bello (Spa) halved with Lee Westwood (Eng)
Jon Rahm (Spa) lost to J.B. Holmes (US) 2&1
Matt Kuchar (US) bt Si Woo Kim (Kor) 6&4
Patrick Reed (US) halved with Shane Lowry (Irl)
Sergio Garcia (Spa) bt Andrew Putnam (US) 5&4
Dustin Johnson (US) lost to Branden Grace (Rsa) one hole
Hideki Matsuyama (Jpn) halved with Chez Reavie (US)
Tommy Fleetwood halved with Kyle Stanley (US)
Louis Oosthuizen (Rsa) bt Byeong-Hun An (Kor) one hole
Bryson DeChambeau (US) lost to Kiradech Aphibarnrat (Tha) 2&1
Marc Leishman (Aus) bt Russell Knox (Sco) two holes
Tony Finau (US) lost to Kevin Kisner (US) two holes
Ian Poulter (Eng) lost to Keith Mitchell (US) one hole
Brooks Koepka (US) lost to Haotong Li (Chn) one
Alex Noren (Swe) bt Tom Lewis (Eng) 4&2