Woods parred the 16th to remain tied with Garcia, and it was at the island green 17th that the tournament turned in Woods' favor. He made par from 47 feet out, then headed to the 18th.
As Woods was playing the final hole, Garcia rinsed not one, but two balls in the drink at 17. If that weren't enough, the Spaniard also found water off the 18th tee and he would end six back.
Woods parred the last, and it was up to David Lingmerth, who shared the third- round lead with Woods and Garcia. Lingmerth had a 12-foot birdie putt at the last to force a playoff, but he failed to convert.
The win for Woods was his second at this event and 78th on the PGA Tour. He picked up one more win later last year, but has been held to four starts this year due to a bad back.
With Woods out of action, only seven of the last 11 winners of this event are in the field this week and that includes Garcia, the 2008 winner, 2012 champ Matt Kuchar and 2007 victor Phil Mickelson.
With Woods and Jason Day among those on the shelf due to injury, this week's field boasts 46 of the top 50 in the world. Among that group, Masters champion Bubba Watson returns to action for the first time since winning his second green jacket.
Golf Channel will have full coverage the first two days and early action on the weekend before handing off to NBC.
The PGA Tour returns to Texas next week for the HP Byron Nelson Championship, where Sang-Moon Bae rallied past Keegan Bradley to win the title last year.
MADEIRA ISLANDS OPEN, Club de Golf do Santo de Serra, Madeira, Portugal -- The European Tour returns to Europe for the first of five straight events on that continent.
American Peter Uihlein opened the tournament with an even-par 72 last year, then went 15-under par over the final three rounds to win for the first time on the European Tour.
Uihlein will not defend his title this week. He has missed the cut in eight of his last nine worldwide starts. Uihlein and 2012 winner Ricardo Santos both went on to become the tour's Rookie of the Year.
This is a big week for the European Tour as this marks the 1,500th official event in tour history.
The European Tour moves to Spain next week for the Open de Espana, where Raphael Jacquelin needed nine playoff holes last year to beat Maximilian Kieffer. Felipe Aguilar was knocked out on the third extra hole.