The teams were scheduled to play again on Monday night to determine the regional champion.
Koch struck out seven and allowed two hits in his longest outing in 26 appearances this season.
Daniel Sweet and Chane Lynch each singled home a run in the first inning for host Dallas Baptist (46-14). After that, the Patriots left 15 runners on base.
Fourth-seeded VCU (38-23) scored in the second inning on a walk, a single and a double-play grounder.
In a must-win situation, Koch (3-2) relieved starter Dalton Higgins with a runner on second base and one out in the fifth. The right-hander retired the first two batters to end the threat.
Matt Blanchard (2-4) was the losing pitcher.
The winner of Monday's second game would meet Miami or Columbia in a Super Regional.