Greg Halford headed the home side in front, but Wootton levelled things up before Elliott Ward powered home from a corner in the last 10 minutes to hand Alex McLeish his first victory as Forest boss.
Posh made three changes with loanees Wootton and Davide Petrucci making debuts, while Dwight Gayle was also drafted in up front.
Forest should have taken the lead as some good play down the left released Dan Harding and his cross found Radoslaw Majewski, who skied the ball over from eight yards.
And they went ahead in the 27th minute as Halford rose and got a powerful header to a Lansbury corner which looked to have been cleared off the line, but the referee's assistant gave the goal. There were few complaints from the visitors.
Posh could have been level moments later as Petrucci found himself in plenty of space on the edge of the box, but he snatched at his shot and sent it wide.
Darren Ferguson brought on 17-year-old Jaanai Gordon-Hutton after 57 minutes in an attempt to spur on his side, who were having plenty of possession but failing to do anything with it.
And the equaliser came three minutes later as George Boyd's corner hit Lansbury and fell kindly for Wootton who hammered home from close range.
George Boyd then unleashed a shot from 20 yards, but it was easily gathered by Karl Darlow.
McLeish's men grabbed the winner seven minutes from time as Majewski swung in a corner which Ward powered home with his head.