He narrowly beat Tiger Woods and Patrick Reed by one stroke each despite Woods' insane 44-foot birdie putt on the 17th hole on Sunday that put him in contention for his first PGA Tour victory since 2013.
He couldn't convert birdie opportunities from within eight feet on his next two holes, and his lone bogey of the day at 13 saw him briefly drop three behind Conners - who had just made his sixth birdie of the day at 12.
Tiger Woods looks to win his first tournament on the PGA Tour since 2013.
Asked how he felt being in contention for a first victory in nearly five years, Woods added: "It felt very comfortable".
The Englishman notching seven birdies and a single bogey to post an early clubhouse lead that was good enough to see him home for only his second PGA win and his first in nine years since the 2009 Houston Open.
"It was a tough week on a demanding course and I felt I held up really well", said Woods.
Woods, now up to 43rd on the FedEx Cup standings, said he would take major confidence away from his best overall display of the year. "I didn't make a good turn and when I do that, I pull it". I'm finding the rhythm of the rounds, I'm hitting shots, I don't have a problem posting scores. Although they weren't long putts the putts on all three, par putts on 16, 17 and 18 were tricky little things, right to left, dead straight and then left to right. "I played conservatively into the green because I wasn't as sharp as yesterday".
Conners carded 4-under to lead by one shot entering the second round.
Photo The last time Tiger Woods won the Masters was 2005, when Phil Mickelson slipped the green jacket on him.
"I'm going to try to beat all these guys".
He missed birdie chances on both par 5s on the back nine, pulling a wedge into the rough at No. 11 and three-putting from 80 feet on No. 14.
"I felt very comfortable, " he said.
Woods' 34-foot putt on 18 to force a playoff with Paul Casey came up just short. It was going to come down to the final hole at Innisbrook's Copperhead Course, with Woods in the middle of it all.
Woods now heads to Thursday's starting Arnold Palmer Invitational as favourite and in an event he's won on eight occasions including back-to-back success in 2012 and 2013. I know what it's like.
"Everyone loves a comeback story, and the underdog, and Tiger became the underdog", Begay said. "I was kind of getting a little frustrated". "I didn't feel that sharp with my iron game".
Woods, 42, ranks second all-time with 79 PGA Tour titles but has been injury-plagued in recent years.
The 55-year-old Hall of Famer edged Tommy Tolles, Tom Pernice Jr. and Scott McCarron to win for the first time as an individual on the PGA Tour Champions.