The visitors were up against it from the ninth minute when Lewis Emanuel was sent off for fisting away a goalbound header from Riccardo Scimeca.
Bluebirds skipper Darren Purse slotted the resulting spot-kick into the net and City were on their way.
Paul Parry scored a second on the half-hour and, although Rowan Vine pulled one back in first-half stoppage-time, two Michael Chopra strikes in the second period gave the Bluebirds a deserved victory.
Cardiff showed one change from the side which were held to a 3-3 draw at Plymouth with Glenn Loovens back after suspension in place of Roger Johnson.
The Hatters fielded the side that drew with Colchester as former Bluebird Richard Langley returned to Ninian Park.
The game turned in Cardiff's favour when a Parry corner was headed goalwards by Scimeca. Emanuel appeared to fist the ball away and, although the referee allowed play to continue, his assistant flagged for the offence.
Once Purse had put away the spot-kick, Cardiff piled forward in an attempt to put the game beyond the Hatters.
They should have added a second in the 28th minute when Chopra sent Stephen McPhail clear but Hatters keeper Marlon Beresford stretched to block his shot.
Two minutes later the second goal did arrive with a superb strike by Parry. Chopra sprinted through the middle and released the winger who curled a left-footed shot into the far corner of the net.
Luton resorted to heaving the ball out of defence and their front two of Sam Parkin and Vine caused problems for the hosts. However, it came as a shock as the first half drew to a close when the City defence stood off and Vine hammered a low shot into the net from close range.
Luton started the second half boosted by that goal and Leon Barnett powered a header from a Langley corner goalwards but Neil Alexander gathered under the crossbar.
City restored their two-goal lead on the hour with a superb strike from Chopra. McPhail hit a cross-field pass to Steven Thompson who headed back across goal for the onrushing Chopra to rifle home.
Chopra was on the mark again in the 77th minute when substitute Malvin Kamara crossed from the right and the former Newcastle striker beat his marker to the ball before side-footing home from close range.
There was still time for Chopra to go close as he looked for his hat-trick but the Luton defence held out.