The 43-year-old Texan set the record in his home state, finishing with a 72-hole total of 26-under-par 254.
Armour eclipsed Mark Calcavecchia's aggregate record of 256 --established at the 2001 Phoenix Open -- at the par-70 LaCantera Golf Club and earned the $630,000 first prize.
Calcavecchia finished the Phoenix Open at 28-under, blistering the par-71 TPC of Scottsdale.
Armour had rounds of 64-62-63-65.
Defending champion Loren Roberts and Bob Tway shared second at 19-under 261.