The win allows UCI (38-20) to remain alive in the double-elimination format.
The No. 21-ranked Anteaters will meet LSU (41-21) today at 2 p.m. in another elimination game.
Should UCI win today, it would advance to face UCLA (45-13) tonight at 6 in the first of what could be two regional title games.
Should UCI win twice today, it would meet UCLA Monday at 6 p.m. for the right to advance to a Super Regional.
Gillespie said freshman Evan Brock would start today's first game, with senior Eric Pettis set to start today's potential second game.
Gillespie said Bergman, and perhaps senior All-American ace Danny Bibona, who was roughed up in his first start in four weeks in Friday's 11-10 setback in 11 innings to LSU, would be ready to anchor an "all-hands-on-deck situation" on Monday, if necessary.
"That was strategery," Gillespie said of the decision to lift Bergman after five innings. "[The coaches] argued with ourselves whether to get Bergy out of there even a little earlier, but we decided to leave him in one more inning."
Bergman, who allowed five hits, walked one and struck out four. He yielded one run in the fourth to end his scoreless streak at 27 2/3 .
Bergman earned the win to improve to 9-3 and is now 7-1 with a 2.18 earned-run average in his last 10 starts. He has won his last four starts, allowing one run in 25 innings during that span (a softball-like 0.36 ERA).
But Bergman was only part of the story for UCI, which has now produced 29 runs and 39 hits in two regional games.
After two Kent State errors led to five unearned runs in the UCI first, the Anteaters continued to pile on the Golden Flashes (39-25), who were outscored, 34-10, in two games to earn their ticket back to Ohio.
"Bergy was real good and we got a couple big breaks in that fist inning," Gillespie said. "That allowed us to get us off to a five-run start and then, down through the lineup, we did some hitting."