Woods captured the same tournament three times in row for the first time in his already historic career, and became the first player to accomplish the feat since Tom Watson won consecutive Byron Nelson Classics from 1978-80.
The victory also marked Woods' fourth win in his last five starts on the PGA Tour. He posted his 28th career victory to pass Lee Trevino on the all-time win list.
Stewart Cink finished alone in fourth at nine-under par, one shot ahead of Toru Taniguchi and Vijay Singh.
Woods began Sunday's final round one shot behind Azinger after they and 23 others finished their third rounds Sunday morning due to a six-hour weather delay on Saturday. Azinger extended the lead to two strokes with a birdie at the first hole but Woods cut the lead to one after a birdie of his own at the next.
The par-five fifth hole proved to be the turning point in the tournament. Azinger missed his approach left and landed in water. Woods had 240 yards and nailed a three-iron six feet right of the hole. Azinger missed a 15- foot par save and Woods ran home the eagle for a three-shot swing that translated into a two-shot lead for the World No. 1.
'With Paul hitting the water I needed to get the ball on dry land anywhere,' said Woods, who added to $738,000 to his tour-leading earnings. 'I was able to do that and just luckily made three.'
Azinger carded his second bogey in a row at six. Woods then took advantage of the next par-five, the seventh, when he hit his second on the right fringe and chipped to three feet to set up a birdie that padded his cushion to a commanding four strokes.
Woods committed his only mistake of the round at the eighth when his tee shot landed in a bunker. He blasted out to 12 feet but could not save par.
At the par-three 12th, Woods knocked a seven-iron to 25 feet and drained the birdie putt for a five-shot lead. Woods added back-to-back birdies at 14 and 15, the latter after roping a two-iron 15 feet short of the stick.
Woods narrowly missed birdie on 17 as his 15-foot try stopped one revolution short of the cup. He went on to par the final hole after his ball popped out of a greenside bunker.
'I feel like I'm playing well,' said Woods. 'I drove the ball pretty decent this week but I really hit my long irons well. When you get greens with this much undulation and this speed, to roll hit it the way you want to how you want to, that's what it's all about.'
Woods, who will be taking this coming week off before defending his U.S. Open title at Southern Hills, offered his philosophy on how he can come out on top again.
'Hit it straight,' said Woods. 'If you get the ball in the fairway in any U.S. Open consistently, I think you're going to have a wonderful chance of winning.'
Garcia recovered from back-to-back bogeys at five and six with a pair of birdies at the next two holes. He posted a one-under 71 for his second runner-up finish to Woods, the last coming in the 1999 PGA Championship.
Azinger, who won this event in 1993, could not recover from the pair of early bogeys. He added bogeys at 11 and 14 but matched Garcia for second place with a birdie at 15. Azinger had a chance to take sole possession of second but could not convert a birdie putt at the last.
Stuart Appleby, who played with Woods and Azinger in the final threesome, was in the mix until the 12th. He chipped his second with a three-wood into the water and then whiffed on his fourth shot. After finally chipping on to the putting surface, Appleby two-putted for quadruple-bogey seven.
Appleby posted a two-over 74 to finish tied for seventh with close friend and fellow Australian Robert Allenby and Kenny Perry at minus-seven.
Scott Hoch posted his fourth consecutive finish in the top-11, taking 10th place at six-under 282.