First-half goals from Bakary Sako and Leigh Griffiths, his 10th of the season, came either side of a Prince Buaben strike for Carlisle.
However, Wolves surrendered their lead early in the second half to a Liam Noble penalty and it was Carlisle who came close to inflicting only a second defeat of the season on their opponents with the better chances.
Wolves made early inroads into the Carlisle defence and their eighth-minute opener was a classic of simplicity with Griffiths sending Sako clear with a clever pass.
Sako needed no second bidding as he drilled an accurate low shot into the bottom right-hand corner from the edge of the area.
Carlisle’s determined efforts paid dividends in the 30th minute when Matt Robson cut inside to feed Buaben and the former Watford midfielder, on his first home start, curled a delightful right-foot shot into the top right-hand corner from 18 yards.
Sako beat Mark Gillespie with a rocket shot which came back off a post only for the goalkeeper to recover and deny Kevin Doyle’s follow-up.
However, there was no holding Wolves in attack and three minutes before the break Griffiths restored their lead with a far-post header from Scott Golbourne’s cross from the left, the ball finally trickling over the line after striking both posts.
Carlisle drew level for the second time eight minutes into the second half when Noble sent Carl Ikeme the wrong way from the penalty spot after Lee Evans had bundled Buaben to the floor as he prepared to shoot from a position inside the area.
Lewis Guy and Buaben missed clear-cut chances as Carlisle applied pressure although they survived a late scare when Jamie O’Hara’s effort rolled right across the face of goal.