It was the first RBI in 10 weeks for Garza, who was in his fourth game back after breaking his wrist in early February.
Chavez, who has missed nearly three weeks with a back problem, lifted the scoring fly ball to center as a pinch-hitter. It was his first RBI in a month.
Garza, who was two for four to join Cho (two for five) as Pirates with multiple hits, said Thompson's performance was inspiring.
"He's unbelievable," Garza said of Thompson, who lowered his earned-run average to 1.69. "Any time we get him up on the mound, we're always going to have a good chance to win.
"He knows we're there for him emotionally. He's our teammate. He's our brother, so we just back him up any way we can."
Evans, who earned the save in Friday's opener, entered with the bases loaded and one out in the eighth. He struck out the next hitter and ended the inning on a fly ball to center field.
A pair of singles and an error loaded the bases in the Hancock ninth, but Evans preserved the shutout for his seventh save of the season.
OCC, making its fifth straight postseason appearance, is 8-0 in four regionals during that streak. The Pirates lost the play-in game last season and did not advance to a regional.
Southern California Regionals
Orange Coast 3, Allan Hancock 0
SCORE BY INNINGS
OCC 001 000 020 – 3 7 1
AH 000 000 000 – 0 6 1
Thompson, Vandernaald (8), Evans (8) and Woodward; Sechler, Shrider (8) and Young. W – Thompson, 4-0. L – Sechler, 5-4. Sv – Evans (7).