Did Jack ever beat Trevino in a head-to-head?
The closest would've been the 1970 Open Championship, led by Trevino at 208 after three rounds at TOC. Jack was two strokes back. Trevino played quite poorly, with a 77, to end up T3 and two strokes out of the playoff. Sanders and Nicklaus both shot final round 73s to tie in the end, one of the few majors that was arguably "given" to Jack, given Sanders' missed two-footer on 18.
The US Open at Baltusrol, next to Jack winning by four with his famous last-round 65, was also Trevino's coming-out party. He was pretty unknown at the time, and finished 5th, but nine shots behind Jack (he was four back of Jack at the beginning of the final round).
Jack also beat out Trevino at Pebble in '72. Jack was the 3rd-round leader at 216, with Trevino in close pursuit at 217 (I think they may have played that final round together). Jack shot 74 in tough conditions to win; Trevino a 78 to finish five back and T4th.
Trevino was 4th at Turnberry in 1977, but well behind the Watson-Nicklaus duel.