The winger whipped in fierce shots in either half to condemn former Imps boss Keith Alexander's Posh men to a second successive home defeat.
The 23 year-old one time Aston Villa trainee made sure the first half belonged to Lincoln, although Posh recovered from the shock of falling behind to haul themselves back to level terms three minutes before the break when Peter Gain netted against his previous club.
Lincoln gave an early indication of their attacking intent with Lee Beevers getting forward to test goalkeeper Paul Rauchubka who was making his debut.
He was deputising for the injured Mark Tyler on an emergency loan deal from Huddersfield Town that was only sanctioned on Friday afternoon.
Rauchubka safely held that one but the 25 year-old, who saw Premiership action for Manchester United early in his career, was helpless to prevent City grabbing a 22nd minute lead with Amoo confidently putting away his opening City goal after top-scorer Jamie Forrester dummied superbly to allow a Beevers' pass to run through.
Lincoln defender Paul Morgan took the sting out of a close-range effort from Aaron McLean as Posh battled to get back into the picture and Gain was in the right place to poke the ball into the net on 43 minutes following a final pass from another former Imp, front man Simon Yeo.
Posh tried to retain the initiative after the break replacing wide man Adam Newton with Shane Huke in a bid to create a path through the middle, but the Lincoln back line with Morgan and Nat Brown dominant stood firm and little got through to trouble keeper Andy Marriott.
Despite 14-goal Forrester missing a glorious opening to make the points safe, one time Northampton winger Amoo spared Lincoln's blushes with another cracking goal on 72 minutes. He blasted in a low-angled drive from the right after Mark Stallard nodded the ball into his path.