Appleby, the first wire-to-wire winner in Houston Open history, finished at 19-under-par 269 for his second title at this event and the eighth of his PGA TOUR career.
Mathias Gronberg entered the round just two shots behind Appleby, but finished eight shots back in fourth place. He closed with a 1-over 73 to end at 11 under.
Coupled with his third straight victory at the season-opening Mercedes Championships, this title makes Appleby the third player after Tiger Woods and Phil Mickelson to win twice on TOUR in 2006.
'Certainly to win once is nice, and twice is better,' said Appleby, who mixed seven birdies with two bogeys in his final round.
Appleby also became the second Australian to win in two weeks, following Aaron Baddeley's victory at the Verizon Heritage last Sunday. His eight PGA TOUR wins place him in a group that includes Brad Faxon, Lee Janzen, Loren Roberts, Chi Chi Rodriguez, J.C. Snead and Bob Tway.
'[Winning] gives me a dose of confidence to keep moving and do the things that really work,' said Appleby. 'Winning is a very positive thing, and that's why I want to carry it on and take it to the next level.'
Appleby's lead was two strokes after he went birdie-par-bogey on his first three holes. He and Gronberg both rolled in birdie putts at the fourth, and then Appleby began pulling away.
At the par-4 sixth, Appleby knocked a pitching wedge within 14 feet to set up his fourth straight birdie on the hole. Gronberg's approach missed the green, leading to a bogey and a three-shot lead for Appleby at 16 under.
Gronberg had an eagle chip lip out at the par-5 eighth -- 'I couldn't believe that didn't go in,' he said afterward -- and it may have been his last chance to make a run at Appleby.
Both players birdied No. 8, but Appleby went on to birdie the ninth to reach 17 under around the turn, while Gronberg managed only a par to drop four shots off the pace.
Appleby then rolled in a 3-foot birdie putt at the par-four 10th, moving to minus-18 for a five-stroke lead.
His lead was still five shots after 12, and it stretched to seven shots over Estes and Gronberg with a birdie at the 13th. Appleby bogeyed 14, but it didn't matter. He parred out for the win.
Estes carded six birdies and three bogeys in his final round for his best finish of the year. Gronberg, who missed so many opportunities to close the gap on Appleby, ended up with bogeys on three of his final six holes
'It was just nice to play (with Appleby), but unfortunately I couldn't really get my own game going,' the Swede said.
Jerry Smith finished alone in fifth place at 10-under-par 278 after a final-round 72. Mike Weir led a group of five players tied one stroke further back, joining J.L. Lewis, Brett Wetterich, Richard S. Johnson and K.J. Choi in sixth place.
Vijay Singh, who won this event three of the previous four years, recovered from a terrible third round to shoot a respectable 1-under 71 on Sunday. He finished in a tie for 36th place at minus-2.
Singh was the last player to win this tournament by six strokes when he claimed his first title here in 2002.