Boro jumped into the play-off places – with games in hand on their rivals – courtesy of their Weston Homes Stadium demolition job.
Marcus Tavernier fired them ahead with the only breakthrough of a thrilling first half before Wilder’s men really took control after the break.
England Under-21 ace Folarin Balogun doubled their advantage four minutes after the restart and two Boro substitutes got in on the act late on.
Duncan Watmore created a third goal for fellow replacement Josh Coburn with eight minutes to go before capping a terrific away display himself with a ferocious 90th-minute finish.
Wilder said: “We’re in a good position and we’re fighting to try to get back into the big time. I don’t think anyone should back away from that thought process.
“It’s a good day for us getting a result in a difficult arena and now it’s important we carry that on.
“Coming to Peterborough was never going to be as straightforward as some people made it out to be – especially with a defeat at Barnsley still quite fresh in our minds. Our attitude and mentality were really good and they had to be.
“We got a bit sloppy for 10 minutes late in the first half when we couldn’t extend our lead and also gave Peterborough a glimmer.
“But the second goal was huge at the start of the second half and we were then able to bring some good players off the bench to get goals when the game was open.
“The boys at the top of the pitch will get the credit but I thought the back three were outstanding. We were clinical in both boxes and also very good in the bit in between too!
“The standard of training has been spot on during the international break and thankfully we took that into the game.
“We’ve got a huge week with Fulham coming up on Wednesday. They’ve strolled the league really while playing in second gear and it will be a great game.”
Posh boss Grant McCann is refusing to give up on survival despite his side dropping back to the bottom of the Championship.
He said: “It’s a proper learning curve for us. We have to lick our wounds and go again.
“The result is a kick in the teeth but we can’t complain if we make the mistakes we did.
“We had the better of the chances in the first half against a team right in the mix trying to get promoted.
“But we gave them all three of their goals in the second half and you get punished in the Championship for things like that.
“The number of goals the club has conceded this season is ridiculous and it’s something we have to iron out.
“We lacked any sort of conviction, energy and purpose in that second half and that’s unrecognisable from what I’ve seen from us lately.
“We’ll have to learn from it and move on. We get paid to pick the players up and we’re not giving up.”