We have studied the effect of magnetic disorder on the magnetization reversal process in thin Co/CoO films. The antiferromagnetic CoO layer allows a reversible tuning of the magnetic disorder by simple temperature variation. For temperatures above a critical temperature: T-c, we observe a discontinuous magnetization reversal, whereas smooth magnetization loops occur for T < T-c. Our measurements establish the existence of a disorder-driven critical point in the nonequilibrium phase diagram. In addition, we observe scaling behavior in the vicinity of the critical point and determine the critical exponents <beta> = 0.022 +/- 0.006 and beta delta = 0.30 +/- 0.03 for this two-dimensional system.