SYDNEY — The loudest cheers were for Tiger Woods. The Australian Open belonged to Greg Chalmers.

Chalmers won his national championship for the second time today, closing with a 3-under 69 to hold off a late charge by Woods and a 50-foot birdie putt by John Senden that nearly forced a playoff.

Woods had his best chance of winning all year.

“Two holes on the back nine today, and I putted awful yesterday, or I would have been right there,” Woods said.

Two tee shots led to bogeys on the back nine, though he also made birdie on the second-toughest hole at The Lakes on No. 12, then chipped in from just off the green for eagle on the 14th. Woods missed a 12-foot eagle putt on the 17th for a share of the lead.

Behind him, Chalmers made his final birdie with a brilliant tee shot on the par-3 15th hole to tap-in range, then played mistake-free down the stretch and picked up a meaningful par on the par-3 18th with an up-and-down from the bunker.

Chalmers last won the Australian Open in 1998 at Royal Adelaide, a week before the Presidents Cup in Melbourne. He finished at 13-under 275.

Woods’ third place finish was his best result against a full field since he last won two years ago at the Australian Masters.

“I felt great,” Woods said. “It’s nice to finally be healthy again.”