Laird, who birdied the final three holes, finished his third PGA Tour victory at 14-under-par 274 at TPC San Antonio.
The Scotsman earned his third straight trip to The Masters. Laird tied for 20th in 2011 and shared 57th last year in his previous trips to Augusta National.
"Last week in Houston, after I played Thursday, when I didn't hit it well, I went down to the back of the range and hit balls for about four hours with my coach. We got something figured out and I went out Friday and hit great, but missed the cut on the number," said Laird, whose best finish this year before this was a share of 34th at the Arnold Palmer Invitational.
"I felt good coming in here because I really like this golf course. I've played well here a couple years ago. I decided to keep playing aggressive with the way I was hitting hit it. I've putted bad all year, but finally, in the final round, the putter got hot. I can't believe it."
Rory McIlroy got within one of the lead when he birdied the 14th, but ended two back at minus-12 after a final-round 66.
Jim Furyk holed out for eagle on the par-5 18th for a 3-under 69. He shared third place at 11-under with third-round leader Billy Horschel (71) and Charley Hoffman (69), who birdied six of the last eight holes.
Horschel's slow start opened the door for Laird. Horschel stumbled to a bogey at the fourth, but bounced back with a 15-foot birdie putt at the sixth. He remained at 10-under as he parred sixth in a row from the seventh.
Laird was off to a flying start. He birdied the second from five feet out and made it two in a row as his 14-footer at the third found the bottom of the cup.
The 30-year-old converted back-to-back 4-foot birdie putts at five and six to join Horschel in the lead at minus-9. Horschel reclaimed the lead with his birdie at six, but Laird responded with a 7-foot birdie effort at the eighth, which again gave him a piece of the lead.
After three straight pars, Laird drained a 15-footer for birdie on the 12th to go one ahead. He parred the next three before a hot closing stretch.
Laird ran home a 17-foot birdie putt to move two clear of a charging McIlroy, who also birdied the 16th to get back within one. Laird converted a birdie try from off the green at the 17th to regain a 2-stroke cushion.
At the last, Laird ran home a 15-footer for a closing birdie. He walked off with a 3-stroke lead over McIlroy.
"I've been asked probably 30 times the last couple weeks, 'Are you in Augusta?' I've had to say no, and every time I said no, it kind of hurt me a bit," Laird stated. "That was my major motivation to try to get back in tournament's like that."
McIlroy needed to hole his second shot at the par-5 18th to force a playoff, but left that shot 48 feet from the cup. He 2-putted for a closing birdie to end two behind.
The reigning PGA Champion birdied the second and fifth, but stumbled to a bogey on the fourth. McIlroy drained consecutive birdies from the eighth, but he tripped to another bogey at the 10th.
McIlroy birdied the 12th and 14th to get in position, but couldn't overtake Laird down the stretch.
"Over the last three rounds, especially, eliminating the silly mistakes that I was making on the course, the mental errors (was good). To finish off this tournament with a round like today is great going into Augusta," McIlroy said. "Even though I didn't get the trophy ... I'm really pleased with my game. I think this has been a great week for me."
Horschel ended his run of pars with a bogey at the 13th. He birdied 15 and 18 to gain a share of third.
NOTES: Laird earned $1.116 million for the win ... Last year, Matt Every shot 63 to set the course record ... This marked the 11th time a player won the week before The Masters and earned a spot in the field at the year's first major ... The last to do so was Johnson Wagner, when he won the 2008 Houston Open ... With the Scotsman's victory, he stopped a streak of 14 straight Americans winners to start the year, and 16 in a row dating to last year ... Sweden's Jonas Blixt was the last non-American winner, and that came at last year's Frys.com Open ... Next week is the season's first major, The Masters, where Bubba Watson will defend his title.
04/07 19:20:48 ET