A hat-trick from Ivan Toney - he now has 16 goals in 20 starts for the club - and a fourth goal of the campaign for centre-back Rhys Bennett sealed an eighth away win in 13 outings on the road.
Posh moved above Charlton into fifth with this result to leave Evans a happy man. Evans tweaked his formation and personnel after a disappointing Boxing Day loss at Barnsley.
On-loan Tyler Denton replaced Colin Daniel at left-back, while Siriki Dembele was pushed up front in place of Matt Godden. Louis Reed replaced Mark O’Hara in midfield.
“That was dominant, fantastic, outstanding and very professional,” Evans enthused. “I’m so pleased for the travelling fans who saw a poor display at Barnsley. They still travelled up here in good numbers and they must have been pleased with what they saw.
“Accrington are strong at home, but I knew from weeks ago how I would play up here. We played very positively and pressed high up the pitch to force mistakes. We played a midfield diamond at times, and 4-4-2 and 4-2-3-1 at other times, but nothing would have worked if the players hadn’t worked as hard as they did. They were excellent from one to 11.
“We kept a clean sheet against a good set of attacking players and Ivan Toney was again outstanding. We played Siriki Dembele up with him today and told him to use his explosive pace and it worked perfectly.
“Ivan is a dream for a manager. His goals record is brilliant, but his workrate is phenomenal. He is the best defensive header of the ball in the club and he even made one superb tackle in his own penalty area.
“I was pleased for the goalkeeper and the back four, especially Tyler Denton who has had to be very patient this season.
“Our Christmas programme is tough and we won’t be getting carried away with this one result. We need to beat Scunthorpe now as after that we will strengthen the squad and have even more competition for places.
“We go into 2019 in a good place, but we know we have plenty to do to get where we want to be.”
Posh defenders Ryan Tafazolli and Jason Naismith both passed late fitness tests to play. Naismith required a pain-killing injection to get through the 90 minutes.
Posh host lowly Scunthorpe at the ABAX Stadium on New Year’s Day (3pm).