In a match that saw Rovers twice come from behind there was to be last minute drama as Linews bundled home the winner from a corner.
Earlier Ian Harte had put Carlisle in front in the 21st minute. Jo Kuffour levelled on 34 but Carlisle regained the lead when Richard Keogh headed in on 72 mins.
There was to be late drama, Jeff Hughes' 82nd minute chip brought the scores together and just when it looked like a draw was on the cards Lines popped up to send the Cumbrians on a long a depressing journey home.