Australia looks set to take a five-man contingent into this week's Masters after hopes of a last-chance berth faded.
Nine Australians went into the Houston Open seeking the win that would get them to Augusta National.
However, going into Sunday's final round Aaron Baddeley was best-placed but a distant 10 shots behind leader Sung Kang of South Korea.
Baddeley was tied for eighth after a one-over 73 followed a pair of 68s, and needing a final day miracle.
Australians locked in for the Masters are 2013 champion Adam Scott, world No.3 Jason Day, recent Arnold Palmer Invitational winner Marc Leishman, Rod Pampling and world No.1 amateur Curtis Luck.
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Showing the way at the Houston Open is Kang who leads by three shots from Rickie Fowler, who four-putted on the final hole.
Needing to secure a maiden US tour win on Sunday to get to Augusta, Kang fired a one-under 71 to be 17 under while American star Fowler shot a 67.
Already exempt into the Masters, Fowler overcame a seven-stroke deficit to reel in Kang, only to stumble at the end with a bogey at the 17th and a double-bogey at the par-four 18th.
Australia's 2006 US Open champion Geoff Ogilvy had an even-par 72 to be two under in a tie for 32nd while compatriot Matt Jones shot a 73 to be at one under and tied 39th.
