Armour broke the record of 256 by Mark Calcavecchia at the par-71 Phoenix Open in 2001.
Armour finished seven strokes ahead of defending champion Loren Roberts and Bob Tway.
'I'm telling you it was scaring me a little bit,' said Armour, who needed only 108 putts over the four days. 'Every putt went in the hole.'
The victory was worth $630,000, more than double what Armour had earned on tour this year.
Armour shot a 64 in Thursday's opening round on the La Cantera Golf Club course in the limestone hills north of San Antonio. He followed that with a 62 on Friday and a 63 Saturday.
'He's lapping the field here this week,' said Roberts, whose 261 matched his winning score here in 2002.
Armour came into the final round with a string of 81 consecutive holes without a bogey, and he added nine more to that total before missing an 8-foot par putt on the 460-yard 10th. He also bogeyed the 18th after hitting his drive into a bunker.
Duffy Waldorf, who began Sunday's round alone in second, was fourth at 262, while Australian Aaron Baddeley shot 263 and Dan Forsman 264.
Roberts (62), who began the day far back at 11 under, carded five birdies on the front nine. After a bogey 5 on the 460-yard 10th, he birdied the 142-yard 13th before sinking a 32-foot putt for eagle on the par-5 14th to reach 18 under. He finished with a birdie on 18.
Baddeley, two shots behind Roberts at Sunday's start, also shot a 62. He had a 62 in his opening round, but tumbled down the leaderboard with a 70 and a 69 in the middle rounds.
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