The 25-year-old Englishman started the final hole a shot behind Spain's Sergio Garcia and South African George Coetzee, who had set the clubhouse target at 17-under-par, but a 12-foot putt at the par-five 18th handed him a one-stroke victory.
Wood, who fired a majestic six-iron from 202 yards following a booming drive at the last to set up the eagle chance, came home with a three-under 69 while Garcia (66) and Coetzee (65) had to settle for joint-second.
Sweden's Alexander Noren (71) and England's Steve Webster (68) finished four strokes further back on 13-under.
"This win is massive for me. It's taken a huge weight off my shoulders," said Wood, who finished tied-fifth at the 2008 British Open to grab the leading amateur honours and then came joint third at the year's third major 12 months later.
"I've been knocking on the door in previous times and it's not happened. To get it today, to get my first win, it's such an honour. I'm so pleased."
Since he burst onto the scene in 2008, the 1.96-metre Englishman has finished second three times although he won the 2012 Thailand Open on the OneAsia Tour.
Wood had played 115 previous European events without a win and two years ago he squandered a four-shot 54-hole lead at the Iberdrola Open in Mallorca as 2011 British Open champion Darren Clarke won the trophy.
In Qatar Wood was again in danger of letting a lead slip, when his three-shot third-round advantage evaporated as he ran up a double bogey at the par-three third hole after a mishit chip.
Wood's ball hit a brick wall supporting the raised green and bounced back over his head into desert scrubland.
"Making that double bogey was a big setback," said Wood, who will climb from world number 142 into the top 60 when next week's rankings are released.
"I had had a fairly sleepless night. But that turned out to be quite a good fright. It settled me down a bit and I gave myself quite a few birdie chances after that."
Wood produced a sublime chip at the difficult par-four 15th to save par and although he let two good birdie opportunities slip at 16 and 17, his eagle at 18 for the victory led to a flood of messages of support.
"Very well done and congratulations on your maiden victory in Qatar. What a way to finish! All the best for the rest of the season," nine-times major winner Gary Player said on his Twitter account.
Compatriot Luke Donald, the world number three, added on Twitter: "Some finish by Chris Wood to earn his 1st European Tour title - first of many - congrats."
Wood, while clearly delighted and relieved, had some sympathy for Coetzee, who now has 21 top-ten finishes on the European Tour.
"I know how he feels. He has come close a couple of times like I have. So I am sure it won't be long before he wins," said Wood.
Former world number two Garcia, playing his first tournament of the 2013 season, praised Wood for bouncing back after his double bogey early on.
"Obviously he's been trying for a while and he deserves it, and after the start he had today, it's quite impressive for him to come back the way he did and win," said the world number 19.