The 54-year-old Pate, four strokes behind leader Gil Morgan after the second round, breezed to a 5-under 211 total for his first victory in 39 starts and second career Champions Tour title.
Allem (73) and Thorpe (74) each birdied the final hole to tie for second.
Morgan (77), 2006 champion Loren Roberts (71), Wayne Grady (70) and Monday qualifier Robert Thompson (72) tied for fourth, three strokes back.
Relentless tradewinds blew 20 to 25 mph with gusts reaching 35 mph, which eliminated any routine shots. The players scrambled, switched clubs and talked to their caddies, and themselves.
Pate missed a 12-foot putt for par on the 54th hole that would've made him the only player to shoot in the 60s in the final round of the 50-and-over circuit's first full-field event of the year.
With the field struggling just to make par on the Palmer Course, Pate made a mid-round rally with three straight birdies on Nos. 8-10 that pushed him to the top of the leaderboard at 6 under.
The whistling wind forced the 1976 U.S. Open winner to step away before he calmly sank a 4-foot putt on the par-5 eighth for a share of the lead. Pate took the outright lead on the following hole by sinking an 8-footer for birdie.
With everyone faltering, Pate went up by two strokes over Bernhard Langer heading into the home stretch. It became a fight for second when Langer bogeyed 15.
Pate earned $240,000, which tied the largest of his professional career.
It was Pate's first victory since the Outback Steakhouse Pro-Am in the injury-shortened 2006 season where he underwent right-shoulder surgery in the summer to repair torn cartilage. The Outback victory was his first win in nearly 24 years, since the 1982 Players Championship.