The Clarets took advantage of seventh-placed Preston North End's derby defeat to Blackpool earlier in the day to increase their cushion within the top six to seven points, with just four games to go.
After a nervous opening against the managerless R's, in which Rowan Vine came close to scoring on his return from a broken leg, Burnley piled on the pressure.
Jay Rodriguez, on his full debut, was denied a header by Radek Cerny, in the 35th minute and the Czech Republic international goalkeeper was tested three more times before the break.
Robbie Blake's wicked free-kick was between away by the keeper, while veteran Graham Alexander went close either side of that effort.
Burnley picked up where they had left off at the start of the second half and got the breakthrough they deserved on 49 minutes, when Carlisle towered to meet Blake's right-wing corner with a powerful header.
Cerny appealed for a handball by Chris Eagles, who appeared to get the final touch inside the six-yard box, but the goal was allowed to stand.
Carlisle, who scored two goals in two games last month, had been denied by the woodwork from a similar set-piece moments earlier.
The central defender would have made the afternoon even more comfortable with yet another header from a Blake corner with 20 minutes to go, but Hogan Ephraim cleared off the line.
However, Owen Coyle's side had done more than enough to secure another victory which puts them in pole position for play-off action at the end of the campaign.