The 31-year-old Englishman has nine international victories, but had never won in the United States. The victory boosted Casey to No. 6 in the world rankings, a career high.
Casey bogeyed the 18th hole in regulation to complete a 72 and tie Holmes at 11-under par. Holmes wrapped up a 69 almost three hours before Casey finished.
The players met on the tee of the 488-yard 18th hole, the most difficult hole of the tournament with an average score of 4.336.
Holmes hooked his tee shot into the pond that lines the hole up to the elevated green. Casey then drove into the fairway bunker on the right side and hit a safe layup to the front of the green.
Holmes reached the green with his fourth shot, then missed a long bogey putt. Casey two-putted from 27 feet to secure the win.
Wind gusts topped 30 mph on Sunday and blew straight into the players faces on the 18th hole. As Holmes putted on the practice green, Casey hit his 214-yard approach into the greenside bunker.
Casey blasted his sand shot to the bottom tier of the green and two-putted from 36 feet to force the first playoff in Houston since 2005.
Fred Couples, seeking his first victory since winning the 2003 Houston Open, led for most of the final round before bogeys on his final three holes left him at 9-under par, tied with Henrik Stenson and Nick OHern in third place.
Couples and Casey were among six players tied at 11 under when the third round ended Sunday morning. Tour officials said it was the largest logjam at the top after 54 holes since at least 1970, when the statistic was first kept. Bo Van Pelt, Colt Knost and Ryan Moore were also part of the tie, but none of them broke par under the windy conditions Sunday.
Couples birdied the par-5 fourth hole to take the outright lead at 12 under.
Holmes sank birdie putts on the first three holes on the back nine before finding the bunker on the par-3 14th for a bogey. He reached the par-5 15th in two and two-putted to move to 11 under.
I never thought I was out of it, said Holmes. It just takes a couple of birdies.
Holmes hit his approach to No. 18 into the greenside sand trap, blasted out and sank a bending 14-footer to save par.
Its a very intimidating tee shot, Holmes said. After you hit that, the next shot is just as hard, if not harder. If you do bail out, youve got the bunker shot I had. Its not easy.
Casey sank a 10-footer for birdie on No. 12, then pitched to 2 feet on the par-5 13th to tie Couples for the lead. Couples then pulled a 6-foot par putt on 16 and hit the greenside bunker on 17 to start his slide.
The tournament finished in daylight after organizers spent the weekend playing catch-up after high winds suspended the first round on Thursday afternoon.
To save time, third-round threesomes were not reshuffled for the final 18. The leaders teed off again about 90 minutes after finishing their third rounds on Sunday morning.
Its been a long week, Holmes said. I feel like this is the sixth or seventh round. Its just been a difficult week, the way everything worked out.
Casey earned himself some extra rest on Friday when he sprinted from the 17th green to the 18th tee and hit his drive just before play was officially suspended. He played only eight holes on Saturday, then finished a 69 on Sunday morning to begin the final round tied for the lead.
Casey is the first European player to win the Houston Open, but the sixth international winner since 2002. He was one of 37 players who came to Houston to tune up for next weeks Masters, taking advantage of an Augusta-like setup at Redstones Tournament Course.
Greg Norman is also heading to the Masters after fading to an 81 on Sunday. He took a quadruple bogey on the 18th hole, dunking two approach shots into the pond. Sergio Garcia also found the water with his tee shot on 18 and took a triple bogey. He matched Normans 81 to finish 7 over for the tournament.
Padraig Harrington, vying for his third consecutive major at Augusta next week, shot a 77 on Sunday. Harrington hit a pitch shot over the 18th green and into the water. He took a drop, then holed his next pitch for a double bogey. Mark Calcavecchia played nine holes on Sunday, then withdrew with a back injury. John Senden had a streak of 292 holes without three-putting snapped when he needed four putts on No. 16 on Sunday.