It was a first league win over them in 15 attempts and Stags' last win over Stanley came in March 1961 against the previous incarnation of the club.
Davis Keillor-Dunn put them on their way with a stunning overhead kick in the first half and George Maris added a second soon after before Aaron Lewis added a 45 yard wonder goal after the break as Stags remain unbeaten after the first nine games.
Boss Nigel Clough made two changes from the side against Bradford City last week.
Lewis was back into the starting line-up after returning from injury to replace Ollie Clarke, whilst James Gale came in for Swan up front.
There was a scrappy start to proceedings in sweltering Lancashire conditions.
Jordan Bowery created a moment for the visitors but Maris nodded his cross into no man’s land.
Stanley threatened to take the lead as Birmingham City loanee Josh Andrews headed just wide before the players took the first drinks break.
After a stale opening half an hour, the Stags took the lead in some style as Keillor-Dunn used his chest to control Gale’s cross before unleashing a breathtaking overhead kick.
And after hitting the front the Stags doubled their lead seven minutes later.
It wasn’t a goal to rival the Scot’s super strike but they all count as Maris completed a decent move which started with Lewis slipping the visitors in down the right and Keillor-Dunn pulling back a low cross.
Stags’ stopper Christy ensured Clough’s charges went into the break with a two-goal cushion as he kept out Jack Nolan’s powerful 25-yard drive deep in first-half stoppage time.
Dangerous Keillor-Dunn went close to a second five minutes into the second half but was thwarted by Toby Savin.
Nolan squandered a great chance to get Stanley back into the contest when he fired wide from inside the box after Lewis Brunt had given the ball away when bringing it out.
Sub Hiram Boateng failed to test Savin as his curling effort flew narrowly wide.
But the returning Lewis wrapped up the points with 15 minutes to go with first-time strike from a poor Savin clearance.
With the keeper out of position, Lewis simply cushioned it back goalwards from 45 yards and found the open goal with a fantastic finish.
Substitute Swan was denied by a good Savin save at the near post in the ninth minute of added time as the sides were forced to play an additional 16 minutes following a supporter needing medical treatment after taking an Accrington clearance into the stand in the face.
ACCRINGTON: Savin, Mellor, Hills, Rich-Baghuelou (Gubbins, 67), Longelo, Conneely (Woods, 90+5), Coyle (Adedoyin, 77), Nolan (Lowe, 90+6), Leigh, Whalley, Andrews. SUBS NOT USED: Quirk, McIntyre, Woods.
STAGS: Pym, Bowery, Flint, Brunt, MacDonald (Cargill, 78), Reed, Lewis (Williams, 90+2), Maris (Boateng, 57), Keillor-Dunn (Swan, 77), Gale, Akins (Clarke, 90+2). SUBS NOT USED: Flinders, O'Toole.
REFEREE: Ross Joyce
ATTENDANCE: 3,094 (1,034)