The Lions, suffering what could be seen as an FA Cup hangover, were second best for the majority of the game at the New Den and their evening was compounded when Shane Lowry was sent off in the second half.
Lee Tomlin bagged a brace and George Boyd pulled the strings for Posh, who leapfrogged Bristol City to move to within five points of safety. Tomlin stuck early with James Henry equalising for the home side before Tommy Rowe and Nathaniel Mendez-Laing scored either side of a second goal from Tomlin and Boyd capped a wonderful display by adding a fifth late on.
The visitors took the lead in the seventh minute as Boyd controlled the ball in the penalty area before cutting it back into the path of Tomlin, who rifled past David Forde for his ninth goal of the season. The equaliser soon followed as Lowry released Henry who lofted a beautiful chip over Robert Olejnik for his third goal in as many games.
Posh looked sharp whenever they attacked and took the lead for a second time 13 minutes before half-time with Boyd again the architect. The 27-year-old showed a mixture of determination and skill to beat Millwall right-back Adam Smith, showing good awareness as he rolled the ball into the feet of captain Rowe who arrowed Posh back in front.
The game settled into a rhythm in the second half with neither side forcing the issue until an error by Millwall defender Karleigh Osbourne let Posh in for their third goal.
Osbourne played a pass across his defensive line that was too short and Peterborough reacted quickly with Kane Ferdinand robbing Jimmy Abdou of possession and Tomlin was again on hand to finish another perfectly-weighted Boyd pass.
The Posh fans were soon cheering another goal as Mendez-Laing drifted past two Millwall defenders with ease before unleashing a fierce effort that gave Forde no chance. Andy Keogh bundled home a 67th-minute effort but was flagged offside after Olejnik had palmed an initial shot into his path.
Osbourne then forced the Austrian goalkeeper into a reaction save as the hosts looked to give themselves hope of achieving an unlikely result. That hope was extinguished moments later as Lowry was shown a straight red card by referee Darren Bond for hauling down Dwight Gayle when he was clean through on goal.
Howls of derision rang around the remaining Millwall fans inside the stadium with Boyd grabbing a well-deserved goal to make it 5-1 and to leave Jackett's cup heroes languishing in 14th place in the Championship table.M