Midfielder Stuart Green returned to haunt Carlisle as the Third Division's top and bottom clubs fought out the hugely entertaining draw.
Green had endured abuse from home fans from the first minute, although his boss Peter Taylor admitted he had warned him what to expect.
Hull had been under heavy pressure but broke away in the 82nd minute for Green to sidestep Andrews and fire past Glennon from a tight angle for the equaliser.
In an open first half, Carlisle's Andy Preece headed against a post and Hull's Stuart Elliott smashed a 15 yard shot against Glennon's nearpost.
Green almost gave the Tigers the lead in the 45th minute when a Burgess pass found him clean through, but with just the keeper to beat, he pulled his shot wide of the far post.
Carlisle took the lead in the 55th minute from a corner after Simpson's 25 yard free kick was well saved by Boaz Myhill.
Murphy's corner wasn't cleared by the Hull defence, allowing Cowan to poke the ball through to Preece who shot under the keeper from 10 yards out.
The home side continued to dominate and will be disappointed after spurning several chances with on-loan striker Matty Fryatt the chief culprit.
Despite Carlisle's pressure, Hull looked dangerous on the break and were unlucky in the 74th minute when Burgess robbed Arnison and crashed his shot against Glennon's post.
After the game, Hull boss Peter Taylor said; "Our chances were better and I think we deserved to win, Carlisle played well but I am disappointed with some of our play.
"It's difficult to come here but they are in good form and they've given themselves a chance of survival." Carlisle Manager Paul Simpson said; "It shows how far we've come that we're disappointed with just a point from the game. We had them on the ropes but we didn't take our chances."