The 28-year-old Wagner shot a 1-under 71 to finish at 16 under, two shots ahead of Chad Campbell (72) and Geoff Ogilvy (68). Billy Mayfair and Fred Couples shot 66s and finished three shots back at 13 under. Bob Estes and Charley Hoffman, three behind Wagner at the start of the round, shot 72s and finished four behind.
Wagner had missed six cuts in nine previous starts this year and was ranked 193rd on the money list when he arrived in Houston. He matched defending champion Adam Scott's course-record 63 in the first round, then held the 36- and 54-hole leads at an event for the first time in 44 career starts.
His emotions showed all day, as sweat soaked through his green shirt and he nervously wiped his hands with a white towel before most of his shots.
But Wagner held it together, pumping his fist after sinking a 6-foot par putt on the 72nd hole as his parents and several family members cheered from behind the green.
Next week, they'll be applauding him at Augusta.
While Wagner will play in his first Masters, Davis Love III will miss a major for the first time since 1990. Love had to win to qualify for next week's Masters, but he finished 5 under, ending the longest active streak of major appearances at 70.
Phil Mickelson now holds the longest run of major starts, with 55. Mickelson shot a second straight 71 on Sunday and finished at 6 under in his final tuneup before Augusta.
This day belonged to Wagner, the 13th player to earn his first victory in Houston.
He started the day one ahead of Campbell, then opened a three-shot lead when he sank a 26-foot birdie on the second hole and Campbell three-putted. Wagner led by five after a birdie on the fourth. Campbell hit into the fairway bunker off the tee and bogeyed again.
Campbell drove into the fairway bunker on No. 8, then dumped his second shot into the water, leading to a crippling double bogey. Wagner birdied again to get to 17 under.
Ogilvy birdied Nos. 3, 5 and 8 to move into second place, but Wagner led by four at the turn.
Couples, the 2003 champion when the tournament was played at the members' course across the street, was one of several players who mounted charges on the back nine.
Wagner bogeyed the 10th and Couples and Mayfair both birdied 13 and 15, the last two par 5s, to move to 13 under, tying Ogilvy. Campbell bounced back with three straight birdies on 11, 12 and 13 to get to 14 under. Estes also birdied the 11th and 12th to reach 14 under.
But Wagner hung on, as the players chasing him stalled, one after another.
Couples and Mayfair each parred the last four holes. Estes and Campbell both bogeyed the par-3 16th from awkward lies in the greenside bunker. Ogilvy birdied the 12th, but couldn't muster another one until the last hole.
Wagner left a long birdie putt short on the par-4 17th, but he calmly sank the 11-footer to stay at 16 under. He drove his last tee shot into the fairway bunker, avoiding the ominous pond that runs down the left side of the 18th hole.
He hit his 220-yard approach just short of the green, pitched to six feet and easily rolled in the final putt.
Wagner became the second wire-to-wire winner since the tournament moved to the Tournament Course at Redstone in 2006. Stuart Appleby led from the start when he won in 2006.
Divots: Appleby, last year's runner-up, shot a pair of 70s on the weekend and finished at 6 under. ... Pat Perez shot a 64, the low round of the day and his best round of the year, to finish at 10 under. ... Wagner, born in Amarillo, is the seventh Texan to win the Houston Open.