The DP World Tour Rankings in Partnership with Rolex leader did not get out of the group stages in his debut at Austin Country Club last year and looked to be facing an uphill battle at 1 Down with three to play in Group Three.
But he made a two-putt birdie on the par-five 16th to tie things up and then went 1 Up on the next as the Austrian spun his ball off the green and into the native area on the par-three 17th.
The last was then halved in pars, handing Hovland victory in a match where neither player led by more than one hole at any point.
"You've just got to play well," said Hovland. "Those other guys are not going to back down and there's a ton of birdies out there, even though it is windy, so try to do a lot more of the same but try to avoid the big mistakes, which I did.
"With a wedge from the fairway you can't miss the green and hit it in the wrong spot where you're automatically making a bogey.
"I was a little greedy in spots, so I just kind of need to focus on playing solid golf and putting the pressure on the opponent."
In the other match in Group Three, Will Zalatoris won the first and was never behind, cruising to a 5 & 4 victory over fellow American Cameron Tringale.
"It's huge," he said of his win. "Obviously a nice day, I had a good off week last week with (coach) Josh (Gregory), kind of hit the reset button a little bit.
"I've already seen some progress, so obviously it's nice to kind of get off to the start that I did early on in the match, just played solid.
"It's not easy out here, that's the beauty of match play is we can kind of tuck pins in some spots that we don't see week in, week out, but the tougher the better."
The Englishman was 2 Up after seven but Scott levelled things at the turn and was 2 Up himself with three to play.
It looked to be all over when Rose had to take a drop on the 17th but the 2013 U.S. Open champion incredibly holed his third from the drop-zone for a par, with Scott closing out victory on the last after 18 holes that saw him make four birdies and four bogeys.
"It was a real pillow fight between Justin and I," said Scott. "We gave each other a lot of holes, certainly nothing for me to brag about.
"We've played a lot of golf with each other over the years and we certainly didn't have our best stuff today.
"But obviously I'm happy to squeak out a point and kind of keep my hopes alive for the next couple of days."
Jordan Spieth was also a winner in Group 11, defeating Keegan Bradley 2 Up.
Maverick McNealy was a thumping 8 & 6 winner over Joaquin Niemann in Group 14, where Kevin Na also beat Russell Henley 1 Up.
In Group Six, Luke List beat Justin Thomas 3 & 2 and Kevin Kisner was a 4 & 3 victor against Marc Leishman.