Robert Olejnik had foiled the on-loan Irishman twice before he drilled the ball past the Bairns goalkeeper in the 34th minute after being set up by Morten Rasmussen.
The visitors passed up several further decent chances before Keane grabbed his second in the 79th minute to take the Parkhead club back to within 10 points of SPL leaders Rangers, who also have a game in hand.
Source: PA
Source: PA