St Mirren have now gone nine games since their last win on Boxing Day, although defeat for Dunfermline at Celtic Park keeps the Buddies nine points clear of their relegation rivals at the wrong end of the table.
Saints could hardly be faulted for the start they made as they controlled the opening ten minutes. Top scorer John Sutton made solid contact with a spectacular half volley, but aimed his effort straight at Killie goalkeeper Alan Combe.
The visitors finally sprang into life in the second quarter of the contest with Peter Leven testing home keeper Chris Smith with a dipping right-foot drive from long range.
Shortly before half-time dazzling close control from visiting midfielder Alan Johnston created space for himself ten yards out, but Ian Maxwell somehow managed to block his netbound shot.
Kilmarnock's steady improvement continued as they took the lead early in the second half, Nish exploiting his power in the air to head home a corner kick by Paul Di Giacomo.
Four minutes later Steven Naismith cleverly set up Johnston, but the former Scotland international volleyed fractionally wide.
But with 12 minutes remaining Naismith released Di Giacomo, whose cutback was drilled in at the near post by Nish for the clinching second goal of the game.