The two-time victor on the Web.com Tour parred the final seven holes to card a four-under 68 for a winning score of 17 under par, and Landry was the only player in the field to break 70 on all four days.
"It took a lot of hard work to get to this point", Landry said.
"Made a couple putts and, unfortunately, Zach and Trey kind of had some hiccups there on the front nine and they didn't play it as well as I did", Landry said.
Mullinax's hopes diminished when he chunked a pitch shot at the 17th hole, failing to clear a bunker between his ball and the hole.
Baddeley stormed to the finish line on Sunday with three birdies in his final four holes to post his third 71 of the week to go alongside a Saturday 68.
Walker ended the week in outright fourth on 14 under and one shot ahead of two-time victor Zach Johnson, who ran up a scrappy six at the last to complete a disappointing 72.
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The 30-year-old shot 3-under in the first round and back to back 5-under par rounds to tie for the lead with two-time major champion Zach Johnson after three rounds at -13.
"My aim was to be really good".
"It's unbelievable. It's really nice to be standing with the best players in the world and be on the leaderboard", Niemann told CBS television.
Kevin Streelman (5 under in his final round), Andrew Putnam (3 under) and Chris Kirk (1 under) ended up tied for eighth, seven shots back.
Conners was consistent throughout the event, opening with a 2-under 70 and following that up with a 2-over 74.
Landry, who lives in Austin, first turned heads in the golf world when he led the 2016 U.S. Open at Oakmont Country Club near Pittsburgh after the first round. Having started the day tied for 25th, Mullinax is now in solo third, at 12 under, entering the final round.