Shelbourne - 3 Bangor Celtic - 1: Shelbourne needed man-of-the-match Stuart Byrne's late goal to kill off the challenge of LSL champions Bangor Celtic at Tolka Park on Saturday night to confirm their passage through to the third round.
First-half goals inside a minute from captain Owen Heary and Irish international striker Jason Byrne appeared to end the match as a contest. But Bangor, who had been most competitive from the start, pulled a goal back through Brian Warren on 75 minutes.
Victor Reid shaved a post to frighten Shelbourne before midfielder Byrne headed home on 82 minutes to seal a 3-1 win.
Mark Farren scored twice to top and tail Derry City's 3-1 win over MSL side Blarney United at O'Shea Park. Derry appeared to end any notion of a shock with goals from Ciarán Martyn and Farren inside the opening seven minutes.
But Blarney made a match of it when Stephen Jennings converted a 40th-minute penalty.
Farren finally sealed Derry's passage 10 minutes from time with a penalty after Neil O'Riordan was sent off for pulling him down.
Sligo Rovers also eased through with an emphatic 4-0 win over Carrigaline United at Turner's Cross.
Cobh Ramblers finished with nine men as they crashed 1-0 to Dundalk at Oriel Park. David Breen was sent off for abusive language toward referee Declan Hanney on 15 minutes following the award of a penalty, though goalkeeper James McCarthy the spot kick.
Peter Hynes scored what proved to be the winner 12 minutes later when holding off the challenge of Darren Murphy to shoot home. Cobh substitute Graham Cummins was then dismissed in the final minute for a bad challenge.
Kilkenny City had a player sent off as they lost 2-0 at home to UCD.
Anthony Gorman scored the only goal from a 60th-minute free kick as Finn Harps had to work to beat LSL side Crumlin United at Ballybofey.
Monaghan United ended a run of six defeats to hold Premier Division Dublin City scoreless at Dalymount Park and force a replay at Century Homes Park on Tuesday night.
In the fallout from their 2-1 defeat to Athlone Town on Friday night, Galway United manager Stephen Lally's resignation was accepted by the club on Saturday morning.