Carlisle manager Greg Abbott admitted his victorious side had ridden their luck as lowly Bury staged a second-half fight back.
Carlisle made hard work of beating League One's second-bottom side. They led through Lee Miller's penalty and Matty Robson's strike in the first 10 minutes, but Steven Schumacher sparked a Bury response in the second half, which left Shakers feeling distinctly unlucky not to grab a share of the points.
Abbott said: "It was tough and I told the players to expect the Alamo and that's what they got. We didn't always deal with it well, but credit to the defence. They deserved a pat on the back.
"We possibly got our goals too early. We had a couple of chances to kill them off, but could not take them and rode our luck a bit."
Six points from the holiday programme have helped drag Carlisle away from the relegation struggle, but for a weary Bury outfit the defeat at Brunton Park left them further in trouble.
Carlisle made a dream start with two early goals. The first of them came in their first attack in the second minute when Brad Potts cleverly tricked Efetobore Sodje on the byline, forcing the Bury defender to foul him from behind and Miller hammered the subsequent spot kick low into the bottom left hand corner.
Robson extended Carlisle's lead in the 10th minute, turning adroitly near the penalty spot to drive Frank Simek's cross home left-footed after the full-back had made a raiding run down the right.
Ironically the Shakers could also have scored twice in a blistering opening spell as Hopper's header was pushed on to the crossbar by Carlisle goalkeeper Mark Gillespie and then the on-loan Leicester forward should have done better with a David Worrall cross which he turned wide.
Bury came out much-improved after the break and it was no surprise when former Carlisle midfielder Schumacher pulled a goal back in the 53rd minute, planting a firm header past Gillespie after substitute Sebastien Carole had provided the cross from the left.
Gillespie took the man of the match plaudits with a magnificent second-half showing in which he almost kept out the visitors' attack single handed with a series of last ditch saves.