Sligo Rovers 0 Cork City 1
Denis Behan, sent off in Europe midweek, redeemed himself with the winning goal as Cork stretched their unbeaten league run to ten games.
The sides swapped early chances in an open game.
Cork skipper Dan Murray first had to deflect out for a corner from Romu Boco after an enterprising raid down the right by Seamus Coleman.
But Sligo then had a right let off on nine minutes when topscorer Dave Mooney's toe-poke came back off a post from Darragh Ryan's cross.
It was merely a reprieve as Cork deservedly took the lead on 20 minutes when Behan arrived at the back post to head home Neal Horgan's cross from the right.
Sligo dominated the second half, but neither keeper had a save to make as Cork held on for a big win.