Chalmers won his national championship for the second time Sunday, 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.
The matches return to Royal Melbourne next week, and Woods at least showed that he wasn't a complete waste of a captain's pick by Fred Couples. He not only was the low American by finishing alone in third, he looked good doing it.
It was his best result against a full field since Woods last won two years ago at the Australian Masters.
"I felt great," Woods said. "It's nice to finally be healthy again."
Chalmers finished at 13-under 275.
It was a strong field for the Australian Open, with eight Americans on the Presidents Cup team getting ready for next week. That included Woods, a steady presence on the leaderboard. For Chalmers, satisfaction came from his name on the silver trophy again.
"I don't know if it's extra gratification," Chalmers said of beating a field that included a 14-time major champion. "I've got my name twice on that Stonehaven Cup."
Senden, the 54-hole leader, faltered early but gave himself a chance late with a good pitch across the 17th green for birdie. His long putt on the 18th went over the ridge and broke back toward the high side of the cup but missed by inches. He closed with a 72.
Defending champion Geoff Ogilvy had a 7-under 65 to tie for fourth with Adam Scott (68), Nick Watney (72), Nick O'Hern (72) and Jason Day, who hit his opening tee shot in the water and had a 74.
"If I keep putting myself in these kinds of positions, it's only a matter of time I learn the formula and break through and start to win," said Day, who has only one PGA Tour win in his four years on the U.S. tour. "I'm very positive about where my game is right now."
Six players from the top 10 at The Lakes will be at Royal Melbourne next week for the Presidents Cup.
Woods was within two shots of the lead when he made the turn, having gone mistake-free on the front nine to at least give himself a chance on the risk-reward holes along the back nine of The Lakes.
The task became tougher the way he played the 11th, which ultimately forced a bad decision two holes later.
Woods again hooked his tee shot on the par-5 11th, although with the wind at his back, it sailed over the portable toilet and into a sand dune where spectators had been walking all week. His ball was deep in a heel print, and he played an explosion shot sideways just to get out of that mess. He wound up missing a 7-foot par putt.
He made up for that with an 18-foot birdie on the 12th — one of only five birdies on that hole Sunday — and couldn't figure out how to play the 315-yard 13th. He went with driver for the second straight day, and this time it cost him.
"I shouldn't have gone for it," Woods said. "It's a tough tee shot for me because I'm caught right between clubs. Driver is too much and 3-wood is not enough. I tried to hit a big, slicing driver in there and should have just laid up.
"Unfortunately, I made the wrong decision and it cost me a shot."
He was lucky it wasn't more. The ball barely carried a pond and embedded into the muck about a foot short of the red hazard line. Instead of dropping on the other side of the water, Woods blasted behind the ball to gouge it forward, only it popped up and struck a tree, bouncing behind and nearly in another pond. His chip came up short, and he had to get up-and-down for bogey.
He still made it interesting by chipping in for eagle from just off the 14th green, then reaching the par-5 17th in two with a shot that caught the ridge and settled 12 feet away. With a chance to tie for the lead, Woods missed the putt, then settled for a two-putt par on the 18th hole from about 45 feet.
"Two bad tee shots on the back nine cost me," Woods said.
Even so, there were more positives for him to take out of the week. Coming off another four-week break from competition, he played well enough to win except for not turning his bad round — a 75 on Saturday — into a mediocre round.
It was the first time all year that he had to wait after signing his card to see if his score would be enough. That lasted as long as it took Chalmers to save par from the bunker.
The only other time Woods has featured on a leaderboard Sunday this year was at the Masters, when he was tied for the lead at turn until going even par on the back nine and finishing four shots behind.
Woods has played only four tournaments since then because of injuries to his left leg.
"It's been since Augusta, I had the lead at Augusta on Sunday, that's the last time I've been in that spot," Woods said. "It's been a long time, unfortunately I haven't played a lot of tournaments in between. But it was great to be out there, I had a chance. Unfortunately I didn't post the number I wanted to post."