A hat-trick from Ivan Toney secured the win for promotion-chasing Posh against Stanley.
The Reds had won their previous two games but Toney took his tally to 16 goals for the season at the Wham Stadium as Stanley ended a memorable 2018 with a defeat.
Peterborough came close to opening the scoring within 90 seconds when Toney raced forward and squared the ball to the inrushing Joe Ward who fired wide.
Siriki Dembele forced Connor Ripley into the next save before, at the other end, keeper Conor O'Malley denied Sean McConville in a lively opening five minutes.
Callum Johnson tried his luck from distance but it was over the bar and then, in a goalmouth scramble, O'Malley saved Billy Kee's initial effort before Jordan Clark put the rebound wide.
Posh opened the scoring on 19 minutes when a free kick from Marcus Maddison was headed home by top scorer Toney.
Dembele came close to a second on 25 minutes after weaving in the area but Ripley got a vital touch to his goalbound strike.
Clark headed wide for the Reds from a McConville ball in while, at the other end, Mark Hughes blocked Toney's shot after the striker raced forward.
Toney doubled his tally when he got the ball from a ball over the top from Louis Reed and the striker fired past Ripley on 41 minutes.
He came close to a hat-trick a minute later when Toney got onto the end of another long ball forward but this time Ripley was able to turn it onto the post.
John Coleman brought on Offrande Zanzala after the break with Stanley chasing the game and one of the striker's first actions on 51 minutes was to force a save out of O'Malley.
It was end-to-end with Alex Woodyard firing into Ripley's arms and a McConville curling free kick collected by O'Malley.
Stanley appealed for a spot kick when Clark went down under a challenge in the area on 58 minutes but referee Tom Bramall waved away the pleas.
Zanzala got in the way of a fierce strike from Dan Barlaser as the Reds piled on the pressure but Toney remained a threat, firing over at the other end.
And Posh got their third when Maddison's free kick crashed down off the crossbar and Rhys Bennett bundled the ball home on 67 minutes.
Stanley still looked to get back in it with a Zanzala shot blocked and Barlaser's follow-up over the crossbar.
However, after the Reds failed to clear their lines, Toney celebrated a hat-trick, stooping to head home from close range on 85 minutes.
While it was a disappointing loss, 2018 has been a memorable on for the Reds with promotion to League One in April.