Koch, who finished seven points shy of the single-game record set by Larry Romboski in 1956, made 14-of-20 shots from the floor, including five three-pointers.
The Presidents (0-3) raced out to a 16-7 lead in the first eight minutes behind seven points from junior forward Matt Vorndran (Fort Wayne, Ind./Carroll).
The Battling Bishops trailed by nine points (24-15) with 5:50 remaining in the half, but closed on a 17-6 run to take a 32-30 lead into halftime.
OWU (2-1) scored 14 of the first 18 points in the second half to stretch its advantage to 10 points (46-36) at the 13:43 mark, but W&J responded to tie the game, 56-56, after a jumper by Koch with 7:45 left to play.
Senior guard Ross Rybarcyzk (Oberlin, Ohio/Elyria Catholic) drilled four consecutive free throws to make it a 67-62 lead for Ohio Wesleyan with 2:10 remaining; however, five straight points by Koch tied the game with 45 seconds left.
Junior guard Matt Shirer (Medina, Ohio/Medina) nailed a triple with 30 seconds on the clock for the OWU lead. The Presidents had three three-point attempts in the final 12 seconds, but could not get any to fall and OWU escaped with the win.
Junior forward Ben Chojnacki (Medina, Ohio/Medina) led the Battling Bishops with 16 points and six rebounds, while Shirer finished with 13 points in 13 minutes. OWU shot 34 percent (22-of-64) and held a 38-37 edge on the glass.
Freshman center Josip Lucic-Jozak (Pittsburgh, Pa./Baldwin) totaled 18 points, four rebounds and four blocks for W&J, while Vorndran finished with 10 points, five boards and three assists. Koch and Lucic-Jozak scored all 37 points for the Presidents in the second half. W&J shot 44 percent (25-of-57) and hit 7-of-22 attempts from three-point range.