Reading finished fifth in the Championship after inflicting a fourth successive defeat upon Derby.
In his final appearance Robbie Savage lost possession which led to Simon Church being fouled and Ian Harte put the Royals ahead from the penalty spot.
Jamie Ward levelled with a 25-yard effort off the inside of a post.
A second Harte penalty came back off an upright in first-half stoppage time but Hal Robson-Kanu won it after the break with a close range finish.
There was a chance Reading could have claimed fourth spot had Swansea been beaten at home by relegated Sheffield United but the Welsh club's emphatic win means Brian McDermott's side will face Cardiff in the play-offs.
Savage had already been booked for pulling back Jay Tabb when he was dispossessed by Church, who was brought down by Michail Antonio in the area.
Harte converted for his 13th goal of the season, but though Derby offered little they were level after Ward collected the ball 25 yards out and sent a stunning swerving effort past Adam Federici into the bottom corner.
The Rams had the ball in the net again, only for Stephen Pearson to be flagged offside, while Reading spurned the chance to go into the interval in front as Harte thumped the base of the post with his second spot-kick after Michail Antonio had brought another foul from Ayala in the area.
However the home side warmed up for the play-offs by sealing a morale-boosting victory as Brynjar Gunnarsson won the ball which looped up for Church, and his header found its way to Robson-Kanu who squeezed the ball in via a deflection.