Love, in the championship match for the second time in three years, had a chance to seize control on the 14th hole. Already leading by one, he blasted out of a bunker to 3 feet and had a chance to go 2 up. But his short par putt caught the right lip and spun away, and momentum swung to Ogilvy.
Love lost the next hole when he failed to get out of a greenside bunker, making double bogey. Ogilvy went 1 up on the par-3 16th with a tee shot into 6 feet behind the flag.
They halved the last hole with birdies, giving the 28-year-old Aussie the lead when they stopped for lunch at La Costa Resort, facing 18 more holes with $1.3 million to the winner.
Love had a 1-up lead at the halfway point two years ago over Tiger Woods, although he failed to convert several good chances and it ultimately cost him.
Both players were tentative over the front nine, no one doing anything great or wanting to do anything dumb. As a result, Love and Ogilvy halved the first 10 holes, nine of them with pars.
Ogilvy had to make a 6-foot par save from the bunker on No. 1, and he halved the ninth hole with a 12-foot par putt after hitting from a fairway bunker over the green, catching a poor lie in the rough.
Love had plenty of opportunities. He had seven putts on the first 10 holes that would have won the hole, although only two of those putts were inside 15 feet.
He finally won a hole on the par-5 11th, reaching the green in two and lagging a 45-foot putt to 3 feet. Ogilvy found the bunker and blasted long, down a ridge to 25 feet for a two-putt par.
But it all changed on the par-4 14th. Ogilvy went into the bunker and blasted out to 12 feet, while Love's bunker shot stopped 3 feet below the flag. The Australian missed, and Love was shocked when his par putt caught the lip.
On his next tee shot, Love hit into the rough for the first time and left him a poor angle to the green, sending his approach long into the bunker and leading to a double bogey that squared the match.
Four of the previous seven winners of the Accenture Match Play Championship were leading after 18 holes. Woods (2004), Kevin Sutherland (2002) and Jeff Maggert (1999) all rallied after an 18-hole deficit.
Tom Lehman and Zach Johnson played an 18-hole consolation match Sunday afternoon.
Love was trying to win for the first time since 2003, and a victory would move him back into the top 10 in the world. Ogilvy's only other victory on the PGA Tour came one year ago Sunday, when he won the opposite-field event in Tucson, Ariz. He had a chance to break Maggert's record for playing the most holes in one week at this event (127), having already played 113 holes going into Sunday afternoon.