Maddison was superb throughout the 90 minutes, assisting both of Godden’s goals and terrorising the visitors’ backline from the start as Posh moved level on points with sixth placed Doncaster Rovers.
Godden hadn’t scored since December 15 but struck twice inside 10 minutes. A Ryan Tafazolli own goal six minutes later brought the stunned visitors back into the match before Maddison struck with a free-kick.
A mistake from goalkeeper Conor O’Malley allowed Matt Bloomfield to reduce the deficit again, but Maddison sealed the win with his fifth goal of the season.
Posh made three changes from the side who lost 2-1 against Shrewsbury, with Godden replacing the suspended Ivan Toney, Daniel Lafferty coming in for Tyler Denton at left-back and Callum Cooke replacing Kyle Dempsey in the centre of midfield.
A change of personnel also saw a change of formation with three at the back and Maddison and Lee Tomlin playing just off Godden in a 3-4-2-1 formation.
The new set up seemed to bring the best out of the front men as a thrilling first-half saw Posh score three great goals, but only go into the break one goal up.
Maddison was at the centre of everything, beginning with the opening goal after just seven minutes. After his corner from the left was cleared the ball was played back to him and he fizzed a low ball to the back post where Godden fired in from a few yards out to end his goal drought.
Three minutes later and the same combination made it 2-0. Tomlin’s delightful flick played the ball into Maddison’s path and he slipped in Godden, who held off a challenge to roll the ball past Ryan Allsop in the Wycombe goal for his 16th goal of the season.
The lead was halved after just 16 minutes when Jason McCarthy’s cross from the right was diverted into his own net by the head of the stretching Tafazolli which settled the visitors who threatened to level soon after. However, Samuel fired wide from outside the area and a couple of threatening crosses narrowly evaded the heads of Wycombe players.
Naturally it was Maddison who restored Posh’s two goal cushion. After a cross nearly picked out Godden - and the far corner - he won a free-kick down the right after a poor challenge from Joe Jacobson who was booked. The set-piece was then floated delightfully into the far corner.
But Posh became the first team to concede a goal to a Wycombe player in open play for more than six matches when O’Malley spilled a back-post cross from Nick Freeman, allowing Bloomfield to score on his 500th professional appearance.
The midfielder had previously scored for the Chairboys at London Road 12 years earlier.
The quick tempo continued in the second-half, with Maddison firing tamely wide with his right foot from 25 yards and Tafazolli making a brave challenge to stop Samuel from having a clear sight of goal.
Lafferty was next to try his luck, but his low shot from range was easily held by visiting goalkeeper Allsop.
After a rare lull in the match Maddison then struck again after a flowing counter-attack. Tafazolli won a header which came out to Tomlin who played it to Godden down the left. He found Maddison on the right-hand side of the area where he was able to fire in a shot right-footed into the far corner.
Wycombe, though, were not done and came forward again straight away, but Samuel shot over from inside the area.
O’Malley was then fortunate to escape after spilling a corner, before at the other end Maddison surprisingly missed the target from 20 yards out.
Maddison’s cross from the right was then turned in by Godden, who was judged to be offside, before Tomlin superbly played in Joe Ward who could only shoot straight at the goalkeeper.
The miss, though, did not prove costly as Posh comfortably saw out the win despite a very late header from Adebayo Akinfenwa going over.
Posh: Conor O’Malley, Jason Naismith, Ben White, Ryan Tafazolli, Daniel Lafferty, Alex Woodyard, Joe Ward, Callum Cooke (sub Louis Reed, 70 mins), Lee Tomlin (sub George Cooper 85 mins), Marcus Maddison, Matt Godden.
Unused substitutes: Matty Stevens, Tyler Denton, Rhys Bennett, Kyle Dempsey, Aaron Chapman.
Wycombe: Ryan Allsop, Jason McCarthy, Sido Jombati, Anthony Stewart, Joe Jacobson, Matt Bloomfield (sub Nathan Tyson, 70 mins), Dominic Gape, Curtis Thompson, Nick Freeman, Adebayo Akinfenwa, Alex Samuel (sub Luke Bolton, 86 mins).
Unused substitutes: Marcus Bean, Yves Ma-Kalambay, Scott Kashket, Michael Harriman, Paris Cowan-Hall.
Goals: Posh - Godden (7 and 10 mins), Maddison (31 and 66 mins). Wycombe - Taffazoli own goal (16 mins), Bloomfield (38 mins)
Cautions: Posh - Cooper (foul). Wycombe - Jacobson (foul), Thompson (foul)
Referee: Seb Stockbridge 7
Attendance: 6,484 (556 Wycombe)