Matthew Blinkhorn and Eoin Doyle got the goals for the second successive game, as the Bit O’ Red finally broke down a well-organised Drogheda side in the last half-hour.
Blinkhorn flicked home the first from close range after an initial Jason McGuinness header had been taken off the line.
And Doyle wrapped it up with a close-range second.
Rovers introduced new signing Conor Powell to the home crowd of almost 2,000 at half-time, but it was the first thing they had to be enthusiastic about after a lacklustre opening period.
The Bit O’ Red enjoyed the lion’s share of possession, but didn’t create a decent chance until the 27th minute against a disciplined Drogheda defence led by new signing – and new captain – Dave Rogers.
The chance was created by a Joseph Ndo free-kick after Aaron Greene was fouled by Peter McMahon, but Blinkhorn could only direct Ndo’s cross narrowly wide from a difficult angle.
Another Ndo delivery caused problems on 37 minutes, as Raffaele Cretaro rose highest at the back post, but couldn’t hit the target.
Rovers pressed on in determined fashion after the break and Richie Ryan slapped a free-kick off the post after Blinkhorn had been fouled.
And the opener finally came just before the hour-mark, typically from another Ndo set-piece.
This time his corner was met by a towering McGuinness header, but Philip Hand did manage to clear the ball off the line. Gavin Peers won the rebound, however, and Blinkhorn got the vital touch to direct the ball to the net.
The visitors almost responded immediately when McGuinness and Peers failed to deal with a long ball forward and Daniel Corcoran won possession and released Gavin Brennan.
Luckily for Rovers, ‘keeper Brendan Clarke was quick off his line to make a superb stop at the feet of the attacker.
Drogheda enjoyed a productive spell after this and forced a couple of corners, but, with Clarke and McGuinness commanding in the area, a half-volley well over the top from Rogers was the end result.
Paul Cook sprung John Russell from the bench with 20 minutes left, and his impact was almost immediate, as he flicked the ball past Stephen Trimble from close range, only for Robbie Gaul to clear it off the line.
At the other end, McMahon’s lofted cross picked out Corcoran in front of goals, but he could only direct his header straight at Clarke.
But Rovers sealed the win when Doyle hammered the ball to the net from close range with ten minutes left following another Ndo corner.
Sligo Rovers: 1 Brendan Clarke; 2 Alan Keane, 4 Gavin Peers, 20 Jason McGuinness, 22 Aaron Greene; 10 Raffaele Cretaro (7 John Dillon 65), 15 Joseph Ndo, 6 Richie Ryan (Captain), 12 Alan Kirby (8 John Russell 70), 11 Eoin Doyle; 9 Matthew Blinkhorn (3 Iarfhlaith Davoren 77).
Subs not used: 5 Danny Ventre, 14 Mark McGoldrick, 16 Derek Foran, 19 Ciaran Kelly.
Booked: None.
Drogheda United: 1 Stephen Trimble; 2 Colin O’Brien (12 Robbie Gaul 56), 4 Alan McNally, 5 Dave Rogers (Captain), 14 Philip Hand; 7 Mark O’Brien (15 David Freeman 85), 6 Brian Gannon, 8 Stephen Quigley, 10 Peter McMahon; 9 Daniel Corcoran, 11 Gavin Brennan (3 Cillian Thompson 74).
Subs not used: 13 Aaron Shanahan, 16 Robbie Clarke, 17 Victor Ekanem.
Booked: McMahon (27).
Referee: Paul Tuite (Dublin).
