The pre-season friendly was arranged as part of the deal which saw Boyd join the Tigers earlier this year and was settled by summer signing Figueroa's cracking strike on 22 minutes.
Peterborough had been on top before the only goal, with Emile Sinclair having a shot saved by Steve Harper and Tyrone Barnett missing a golden chance.
Midway through the first half, Figueroa picked up the ball 40 yards from goal and ran towards the penalty area before unleashing a left-footed rocket which flew into the top corner.
Recent signing Danny Graham then headed over for the Premier League club before Peterborough midfielder Grant McCann curled a free-kick over.
Second-half chances were scarce, but Tigers striker Nick Proschwitz saw his header from Robbie Brady's cross ruled out for offside.
Brady then had a low a free-kick smartly saved by Joe Day, while Peterborough were unable to find an equaliser in their final match before Saturday's League One opener at home to Swindon Town.