Goals from Wes Fogden, Eunan O'Kane and Marc Pugh sealed victory for Bournemouth at Carlisle and sent them into the FA Cup third round.
Fogden opened the scoring from the edge of the area before O'Kane doubled their lead from 10 yards.
Carlisle had several chances of their own before eventually pulling one back through Mark Beck's header.
Beck had a chance to equalise late on before Pugh sealed it when side footing home from six yards.
Victory for the Cherries saw them stretch their unbeaten run to 11 games in all competitions.
VIEW FROM THE DRESSING ROOM:
Bournemouth manager Eddie Howe speaking to BBC Radio Solent:
"Full credit to players to come to a really difficult place, and in the weather conditions, the travelling, the players have responded brilliantly to that challenge.
"I thought we controlled the game, we were very brave, we played from back to front. Our goalkeeper's distribution was excellent, our defenders were brave and wanted the ball and I felt we dictated the game"
On Eunan O'Kane's goal, Howe added: "I thought he did really well today.
"He took his goal excellently and he is a very good footballer and he's one we're really pleased with."