Lee's fine finish late in the first half proved the difference at the Weston Homes Community Stadium, as Posh returned to the second tier of English football for the first time since the 1993-94 campaign.
Chris Whelpdale shot just wide before Lee made the all-important breakthrough for Peterborough, five minutes prior to half-time.
George Boyd picked out Lee in the area and the former Tottenham trainee emphatically blasted into the top corner from close range.
Gerken denied Craig Mackail-Smith just before the break after being sent through by Aaron McLean and Posh pushed for another goal in the second half.
Mackail-Smith narrowly failed to connect with McLean's low cross and Gerken denied both Mackail-Smith and Whelpdale before the end, but one goal proved enough for Posh to climb out of League One.