The game started with both sides aiming to outwit each other but failed to convert the few chances that came their way in the first half.
With the game looking to end without goals, Kieffer Moore broke the deadlock in the 87th minute, converting from the penalty spot.
Meite then rescued the Royals from defeat when he found the back of the net moments before the end of the game after receiving a fine assist from Sam Baldock.
The draw helped Reading to avoid their second consecutive loss after losing against Watford in their last outing in the Championship.
The result ensured the Royals are seventh on the league table after gathering 67 points from 41 games and are one place below the play-off spots.