The hosts took an early lead as Mark Davies was allowed to run deep into the Liverpool half before he fired low past Pepe Reina.
Soon after, Bolton doubled their lead as Nigel Reo-Coker burst into the area to strike past Pepe Reina on the half-hour.
As Liverpool looked to be in trouble, they got themselves back into the match on 37 minutes when Carroll flicked on Reina's long ball to Craig Bellamy, who fired past Bogdan.
Liverpool controlled large parts of the match after the goal and almost found a way back in when Daniel Agger's thunderbolt skimmed the top of the Bolton bar.
As Kenny Dalglish's side desperately tried to create something, Bolton held on for the victory.