Wanderers boss Kenny Jackett blasted his team's second-half performance when they allowed Carlisle to come back into the game and almost snatch an unexpected win.
First-half goals from Bakary Sako and Leigh Griffiths, his 10th of the season, came either side of a Prince Buaben strike for the hosts.
However, Wolves lost 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 and would have done so if Lewis Guy and Buaben had taken clear-cut chances.
In contrast to Jackett, Kavanagh was delighted after a run which had seen his team lose three out of their previous four league games.
Kavanagh said: "I'm extremely proud. After some difficult previous games I thought they were absolutely magnificent against a very, very good Wolves team who are flying at the moment.
"We matched them and probably could have won the game. To a man they did their jobs to the maximum.
"There was a lot of quality on show and both teams were going at it hammer and tongs. Both looked capable of scoring on the counter. Putting on a performance like that is special."