Taylor Smith, a 29-year-old tour rookie seeking his first victory, also finished at 21-under, but was disqualified for having an illegal grip on his putter.
Smith was notified of the disqualification on the ninth hole, when he was 18-under and trailing Woods by 2 strokes. Tour officials allowed him to keep playing while he appealed, and he made an eight-foot birdie putt on No. 18 to apparently tie Woods.
Smith had used a 44-inch split-grip putter. United States Golf Association rules state that a putter with two separate grips must have grips that are perfectly round - Smith's are oval shaped and flattened on one side. Smith's appeal to the USGA was denied.
``I didn't care if I didn't make a penny this week, I wanted to get to 22 under par, so that I would know that I won the tournament,'' Smith said.
Said Woods: ``I have mixed emotions. I feel like I should have been in a playoff. I feel bad for Taylor because he played his heart out.''
The $216,000 winner's check gave Woods $734,794 in just seven pro starts. He is No. 23 on the money list, which qualifies him for next week's Tour Championship at Southern Hills in Tulsa, Okla. The win also put him 14th on the Ryder Cup points list.
``He can do things that I can't do,'' said Stewart, who carded a 67.
Woods, who won his first pro title two weeks ago in Las Vegas and finished second last week in the Texas Open, has had an unprecedented run of success since he turned pro eight weeks ago after winning his third straight U.S. Amateur title.
``I was just hoping to get my [PGA tour] card,'' Woods said, standing on the 18th green with the Disney character Tigger.
``I had seven chances, and if I couldn't get my card I was going to go to Q-school [qualifying school],'' he said. ``Luckily, I was playing real well coming off the Amateur.''
Woods had to fight 18 holes against Stewart, a winner of seven tournaments and two major championships.
They began the round at 15 under, 1 off the lead. Stewart hit every green in regulation. Woods missed only one, although he did have three 3-putt bogeys.
Woods took the lead for good on the par-3 12th with a 9-iron from 159 yards that stopped 18 inches from the hole. A 3-putt from 10 feet at the 17th reduced his lead from 2 to 1.
With the gallery five deep on No. 18 and some people sticking their heads through the mesh from under the bleachers, Woods left his 25-foot birdie putt about 18 inches short, then had to wait as Stewart missed his birdie chance.
Woods continued to produce spectacular results. In the 27 rounds Woods has played as a pro he is 95 strokes under par for a remarkable stroke average of 67.89.
The Disney Classic was the last full-field event of the 1996 season. Woods' move to 23d place dropped Lee Janzen out of the top 30 who qualified to compete in the Tour Championship.
Smith was paired with Lennie Clements, who is one of the few players on the PGA tour to use a split-grip putter, and Clements noticed that Smith's grips were nonconforming.
Clements reported it to rules officials, and Smith was told at the turn that he was disqualified. At the time, Smith was a stroke behind Woods and refused to accept disqualification. He asked to play the rest of the round and then appeal.