United have drawn eight of their previous 12 Clydesdale Bank Premier League matches ahead of Tuesday's trip to Inverness and have scored late equalisers in five of those.
The latest was on Saturday against bottom club Hamilton when Andis Shala levelled in the 83rd minute after United missed a number of chances before conceding a penalty 12 minutes before the interval.
Kirk said: "I'm hoping we can get the first goal for a wee change and let other teams chase the game.
"Sometimes when you come back so late in the game it feels like winning. But we have to try to change these one points into three points and get in this top six.
"We've got a hard week coming up next week and we can take the pressure off ourselves by starting winning."
Source: PA
Source: PA