Crouch could only get a slight glance on an almost-plum cross from Mark Gonzalez before his fellow lofty forward Koller forced the match to end level.
Meeting a delivery into the middle from the left flank, the Czech stooped to angle a header beyond the grasp of Reina on 81 minutes.
Koller could have completed a turnaround, too, but he planted a clear chance the wrong side of the left post a minute from full-time.
**Liverpool first half:** Dudek (Westerveld, 23), Wright (Kelly, 15), Skrtel, Hyypia (Vignal, 31), Klavan, Aurelio, Spearing, Biscan, Thiago, Gerrard, Babel (Dowie, 31).
**Liverpool second half:** Reina, Kelly, Klavan, Skrtel (Pennant, 53), Vignal (Benayoun, 61), Thiago, Riera, Gonzalez (Sinama-Pongolle, 74), Kuyt, Schillgard (Crouch, 59), Gerrard (Smicer, 82).
**Attendance:** 60,482