The lead did not last long as MK Dons pulled level seven minutes later through Josh Murphy, who controlled a cross from Church to place the ball past Carson from close range.
Derby were let off the hook moments later as Warnock and Jason Shackell had a mix-up that gifted Church the chance to cross the ball to two open players but he managed to miss both of them.
Carson was there again for Derby after Lewington had a free header saved well by the goalkeeper, who diverted the point-blank effort onto the post.
Paul Clement's men stole back the lead with two minutes remaining after Ince found himself alone on the left before passing the ball across the goal for substitute Bent to slide the ball into an empty net.
The East Midlands club almost threw away the game in the final moments after Carson's punch almost went into his own goal but Andreas Weimann cleared off the line.
Ince finished the game off in the final seconds after MK Dons gave the ball away at the back, allowing the winger to run on and beat Martin one-on-one.
The win lifts Derby into fifth while MK Dons remain just above in the relegation zone of the Championship in 20th.