It was a great comeback from the Warriors, who were beaten 29-14 in France in round 3, and with home games against Bucuresti and Petrarca to come they now look odds on to win the Pool.
Carlisle's boot gave the home side a steady start as he kicked three successive penalties to give the Warriors a 9-0 advantage. Opposite number Sebastien Laloo pegged back the advantage to three points by the break with two goals of his own.
But there was no stopping the Warriors after the break as they scored 18 unopposed points to establish a five point lead over Petrarca and Bourgoin at the top of the Pool table.
Carlisle added two more penalties after the break before centre Sam Tuitupou grabbed the games first try 13 minutes from time. Replacement hooker Aleki Lutui then wrapped things up with a second score four minutes from the end.
Worcester coach Mike Ruddock is hoping to use the Challenge Cup as his side's passport into the Heineken Cup next season. The Warriors were beaten finalists last year, semi-finalist three season's ago and European Shield runners-up the season before that.
Earlier in the day Bucuresti had given Worcester's qualification chances a considerable boost with their 17-15 triumph over Petrarca in Italy. A 74th minute penalty from full back Florin Vlaicu clinched the deal for the visitors after they had matched their hosts try for try.
The Romanians are next up at Sixways in January, although the home side will feel pretty confident having won the game in Bucurest 53-17 in round 2.