Four ahead at the start of another blustery day at the Doral Golf Resort & Spa, Woods ground out a one-over-par 73 to finish on 10-under 278.
The world number one survived three bogeys over the closing stretch to clinch his 56th PGA Tour title and a 13th WGC (World Golf Championships) crown.
It was his sixth victory in the tournament's eighth edition, and his 11th WGC strokeplay title in 16 starts.
U.S. Ryder Cup player Wetterich, Wood's closest pursuer overnight, birdied two of the last five holes for a 71 and outright second place at eight under.
Australia's Robert Allenby, helped by two monster birdie putts, fired a best-of-the-day 67 to share third place at six under with compatriot Geoff Ogilvy (70) and Spaniard Sergio Garcia (70).
"Conditions were not easy and you had to grind it out," Woods told reporters after laying up short of the green in two at the treacherous par-four last where a bogey earned him the winner's cheque for $1.35 million.
"I stayed pretty patient all day and the whole idea was to shoot under par and it would be over. I didn't quite get it done but ended up winning the tournament anyway.
"I struggled a little bit on the greens today, getting the pace down," added the 31-year-old, who took 33 putts for his worst tally of the week.
"The wind was a little blustery and I had a hard time figuring out the grain."
Woods, who won the Buick Invitational in January in his first start of the year, became the PGA Tour's second multiple winner this season after Vijay Singh, who clinched the Mercedes-Benz Championship and last week's Arnold Palmer Invitational.
VICTORY CRUISE
For much of the final round, it appeared Woods would cruise to victory at a venue where he has won the Doral Championship for the last two years.
As the gusting breezes strengthened, he mixed three birdies with two bogeys to reach the turn in one-under 35 and five ahead of the chasing pack.
After picking up his fourth shot of the day at the par-five 10th, where he reached the green in two and two-putted, he was six strokes clear and seemingly in cruise control.
"I stayed pretty patient all day and the whole idea was to shoot under par and it would be over. I didn't quite get it done but ended up winning the tournament anyway.
"I struggled a little bit on the greens today, getting the pace down," added the 31-year-old, who took 33 putts for his worst tally of the week.
"The wind was a little blustery and I had a hard time figuring out the grain."
Woods, who won the Buick Invitational in January in his first start of the year, became the PGA Tour's second multiple winner this season after Vijay Singh, who clinched the Mercedes-Benz Championship and last week's Arnold Palmer Invitational.
VICTORY CRUISE
For much of the final round, it appeared Woods would cruise to victory at a venue where he has won the Doral Championship for the last two years.
As the gusting breezes strengthened, he mixed three birdies with two bogeys to reach the turn in one-under 35 and five ahead of the chasing pack.
After picking up his fourth shot of the day at the par-five 10th, where he reached the green in two and two-putted, he was six strokes clear and seemingly in cruise control.