Striker Mansaram claimed the plaudits for Dundalk’s first goal on 38 minutes, which came about following a terrible mix-up in the Rovers defence.
Burns doubled the lead on 64 minutes when he headed Harpal Singh’s cross past Richard Brush, and Turner then slid home the third after latching onto Mansaram’s pass.
Raffaele Cretaro pulled one back for Rovers, but Owen Morrison blazed a late penalty over the bar to compound the home side’s misery.
Dundalk’s breakthrough arrived when Richard Brush dropped George O’Callaghan’s delivery in the area, and in the ensuing chaos, an attempted clearance rebounded off Darren Mansaram before crossing the line.
Two former Rovers players helped the away side double their advantage; Singh swinging in a free-kick and Liam Burns rising to head home.
They made it 3-0 10 minutes later, when Mansaram slipped a neat pass into the run of Chris Turner, who confidently slid the ball past Brush and into the net. Rovers pulled one back just a minute later when Cretaro managed to direct the ball to the net from close range following Richie Ryan’s industry down the left.
Meanwhile, Waterford United moved up to fourth place in the First Division with a deserved 1-0 win over Longford Town, Willie John Kiely netting after 16 minutes.
The Blues move above Athlone Town who lost 1-0 at home to Wexford Youths, the only goal coming on 73 minutes when a cross from the left was met on the volley by Conor Sinnott who struck home from 18 yards.
Elsewhere, Limerick were held scoreless at home to Monaghan.
SLIGO: Brush, Boco, Peers, Keane (Torpey 82), Holmes, Morrison, O’Grady (captain), Ryan, Doherty (Almeida 61), Cretaro, Feeney (McTiernan 68).
DUNDALK: Bennion, Simon Kelly, Burns, Heary (Shaun Kelly 24), Rogers, Mulvenna (Mackle 68), Daly, Turner, Singh, O’Callaghan, Mansaram.
Referee: N Doyle.