Levet made four birdies and three bogeys Sunday for a 7-under total of 277 to capture his sixth career title.
Martin Kaymer was three strokes back in fourth after a closing 73. The PGA Championship winner will overtake US Open champion Rory McIlroy into third place when the world rankings are published Monday.
Levet, the 2002 British Open runner-up, was level with Olesen until the last hole. Levet hit an approach that landed 4 meters (14 feet) from the pin on the water-guarded green while Olesen cleared the lake but failed to reach the green with his second shot.
Levet missed his birdie putt, giving the Dane the chance to force a playoff. Olesen’s chip landed a meter from the cup but he failed to convert a short par putt. Foster was also in a position to force a playoff but his 6-meter (20-foot) birdie putt on the 18th was short.
Foster took sole possession of the lead in the early afternoon after compatriot James Morrison found the water in his first two holes to drop three shots.
Morrison finished tied for seventh with Hennie Otto of South Africa and Brendan Steele of the United States, five strokes back.
Foster parred his first two holes and the overnight leader had a two-shot cushion when Ramsay bogeyed No. 3.
Kaymer’s chances of victory plummeted when he sent his tee shot into the lake for a double bogey on No. 2 . He slipped further down the leaderboard by missing a shot par putt on No. 6.
Levet showed the best and the worst of his game by missing a 3-meter (10-foot) par putt on No. 2 before holing a birdie putt from more than 15 meters (49 feet) two holes later.
Morrison birdied No. 5 to claim a share of second place, but then hit his approach into a greenside bunker to bogey No. 7. He overhit a chip on No. 9 to drop another shot before two consecutive bogeys after the turn left him out of contention.
Foster played solidly on the front nine.
But he made his first error of the day on the 12th, failing to reach the green. Foster two-putted for a double bogey to open the door for the chasing pack as Levet joined him on top of the leaderboard at 7 under, one stroke ahead of Olesen and Ramsay.
Foster three-putted the 13th to lose the lead.
Olesen birdied the 14th with a chip into the cup to overtake Foster in second place as Levet converted a short birdie putt to reach 8 under and stay one stroke ahead of Olesen.
Levet and Olesen bogeyed the 16th to bring Foster back in contention, while Ramsay found water on the 15th for a triple bogey to drop out of contention.
