City's 4-2 win, their first three-point haul since March, came by way of a second-half hat-trick by Jay Emmanuel-Thomas and Scott Wagstaff's thunderbolt, earning City their first away victory since December.
Carlisle led at half-time through a Sean O'Hanlon header, but Thomas scored twice inside a minute after the break and Wagstaff added a third.
Although Liam Noble pulled one back for the home side Thomas was again on target for City to make sure of the victory in the closing minutes.
It was a return to Carlisle's early-season habit of conceding soft goals, although the Robins were value for their first win in 22 league games.
City assistant John Pemberton said: "At half time the lads got a volley and they came out and responded really well.
"The first half was probably our worst of the season, but in the second half we were very good.
"That will give us confidence. We've been close in a lot of games and have finally got the monkey off our back.
"I honestly think we are in a false position. It's a relief for us and we can start to climb the table.
"Certain things needed to be said and the response of the players was excellent.
"They are honest as the days are long, but you can't keep being unlucky and you have to go out and fight to make things happen."
City boss O'Driscoll gave the post-match press briefing a miss to spent time with his players.
"He was talking about their response and taking a moment with the them," said Pemberton.
Scott Wagstaff, scorer of City's vital third goal, said: "It's massive for us. We didn't play our best, but it was a group effort.
"We knew we were way off the pace at half-time and the gaffer had a few words with us and got us going again.
"The second half was brilliant and the boys showed great character."
In addition to his hat-trick Thomas set up Wagstaff's goal.
"On his day Jay is brilliant and he was excellent," Wagstaff said. "He set me up and I probably owe him a few."