Matthew Blinkhorn's 14th minute strike proved the difference between the sides, although Sligo should have had the result sewn up before the final whistle.
The same sides had met a week earlier at the same venue in the quarter final of the FAI Ford Cup, with Rovers victorious 3-0 on that occasion, but their First Division opponents produced a much improved showing this time out.
Philip Hughes' 25th minute free-kick was the visitors' best chance of the opening half, but it climbed over Ciaran Kelly's crossbar.
Following the interval, Sligo Rovers continued their dominance, with Sava denying Blinkhorn within a minute of the restart and Gavin Peers volleying wide from Joseph Ndo's corner on 55 minutes.
Russell almost sneaked in at the far post for Rovers in the 59th minute, and Eoin Doyle should have made it 2-0 on 65, but pulled his shot wide of the far post.
Against the run of play, United nearly equalized in the 73rd minute - Alan Keane clearing Brian Gartland's header off the line with Kelly beaten.
Rovers responded immediately with Romauld Boco forcing Sava to dive to his left on 74 minutes and Russell almost converting for the home side - the excellent Sava again coming to the rescue.
Rovers substitute Gary McCabe's 85th minute free-kick also crept just past Sava's post, and minutes later Boco dragged a shot wide.
Darragh Hananphy nearly engineered a stoppage-time chance for the visitors - only for Rover's Jim Laughlan to time a saving tackle to perfection - and the hosts held out for victory.
The win gives Paul Cook his first success as Sligo Rovers manager.
Sligo Rovers: C Kelly; A Keane, G Peers, J Laughlan, I Davoren; E Doyle, J Russell (G McCabe 78), R Ryan, R Boco; J Ndo, M Blinkhorn
Monaghan United: G Sava; C McMahon, A Byrne, B Gartland, S Grimes; A Collins, S Brennan (C O'Connor 68), B Clancy, D Tierney (A Lynch 84); K Berminghan, P Hughes (D Hanaphy 77)
Referee: D Hanney (Dublin)
This victory is a reward to the team and especialy Paul Cook who has put in an enourmous amount of work in the last 3 years. Well done the Bit'O'Red!!!!!!!!!