The Blues were in Luton for their second away game of the week on Tuesday evening.
United made three changes for the long trip into the Bedfordshire with Tom Miller, Tom Parkes and Shaun Miller getting the nod to replace James Brown, Kelvin Etuhu and Richie Bennett.
The Blues started well with some good passing from back to front which brought a flick from Shaun Miller as he got up to meet a ball forward from Lambe. Hope tried to chase it down but Stech was off his line quickly to gather it up.
Carlisle came again when Shaun Miller rolled his man on the half way line. He fed Lambe on the overlap and the cross from the wide man had Hope interested. He threw himself at it on the dive, but his header was too close to the keeper.
Match official Chris Sarginson became the most unpopular man in the stadium when he stopped Mpanzu in his tracks after he had gone through a Shaun Miller tackle in full flight. The contact between the players had left the Luton man without his boot, and play was stopped for safety reasons.
The Cumbrians almost took the lead on 12 minutes when a lovely pass from Joyce left Shaun Miller with space to work in. He got it under control and twisted and turned his way to a shooting position, and it needed a touch from a defender to take it over the bar as he set himself to celebrate.
Potts had a shot blocked as the Hatters tried to pick up the pace, but it was the visitors who showed again when Hope contested a bounce ball tight by the left-hand touchline. The striker followed the movement of play, won it back and went for goal with a 25-yard grasscutter. Stech watched as it went past his upright.
Luton got forward with purpose on 19 minutes as they flooded the box with options left and right. Gary Liddle executed an excellent first block, but the hosts came again and Shinnie had time to pick his spot as he bent a lovely effort into the far corner.
The Hatters suddenly looked alive and a reverse pass from Berry put Shinnie into a dangerous position. He clipped his delivery to the back stick, but Hill was there to guide it away to safety. Lee was next to tease a delivery into the area but it had too much on it and Bonham was able to gather it up.
A cross from Mike Jones had everyone waiting to see where it landed, as United started to see more of the ball again, and Stech was relieved to see it dip over his bar.
But the Cumbrians were given a mountain to climb when Sheehan floated a 30-yard free kick delivery towards the six-yard box. Dan Potts timed his run perfectly to clip a header past Bonham and into the bottom corner.
Lambe and Jones had shots blocked when Carlisle attacked from the restart and Tom Miller was disappointed when he sent a follow-up volley high over the target. There was more good Carlisle pressure when a fierce shot from Jones was blocked. Joyce was there to play Hope into space and he spun quickly to help the ball on its way. Stech stopped it but he had to recover quickly as Shaun Miller tried to finish off the loose pieces.
United switched to 4-4-2 after the break, with Etuhu on for Parkes, but it was Luton who piled on the early pressure as they tried to put the game to bed. United had other ideas and crosses from Liddle and Grainger had to be dealt with as they tried to find the magic ingredient.
The Carlisle goal was threatened ten minutes into the half when Mpanzu found himself with the ball at his feet from a deflected Shinnie pass. He put everything into his volley but Hill did enough to get his body in the way at the vital moment.
Hope was wayward with a shot from distance when he had blue shirts screaming for a pass, and Grainger had a 19-yard free kick blocked before he horribly miscued the volley away from the target.
United had half a shout for a penalty when a shot from Miller went into the air on the spin. Lambe appeared to be held back as he tried to get on the end of it, but the officials showed absolutely no interest at all.
A loud call for handball was ignored when a toe poke from Jones struck a defender, and Miller was robbed of the opportunity of a shot when he came under pressure with his back to goal just nine yards out.
Jones started to shoot on sight and he won his side a corner when another effort took a touch and bent over the bar. Carlisle started to play some good football and Joyce and Liddle combined to put Lambe through with Luton looking uncomfortable. Another corner was flicked goalwards by Joyce but it somehow stayed out with Stech well beaten.
Grainger was next to go close when he worked a free kick routine with Jones. The roll of the ball invited the shot but it was straight at Stech and he held it close to his chest. The Carlisle dominance was made to count for nothing with 14 minutes left to play when, with men committed forward, substitute Harry Cornick found himself with a clear run at goal. He had Hylton in support, but he didn’t need him as he drew the stopper and slotted it home.
The home side were then given a penalty when Hylton went down under pressure from Hill, but Bonham went the right way and made an excellent save to deny the same man from the spot.
Luke Joyce then had to help his defence out when a downward header beat Bonham. The midfielder kept his eye on it and hooked it off the line with Shinnie ready to celebrate.
Bennett dragged a shot on the spin wide as the clock ticked down, and both Shaun Miller and Hope scuffed difficult volleys, but the points were destined to stay in Bedfordshire as Luton saw the game out to strengthen their promotion credentials.
Luton Town - Shinnie (19), Potts (30), Cornick (76)
Luton Town - Sheehan (45), Mpanzu (70)
Carlisle United - Hope (45), Joyce (51), Grainger (90)
Luton Town - Stech, Potts, Mullins (D'Ath 82), Stacey, Hylton, Shinnie (Famewo 88), Rea, Mpanzu, Berry, Lee (Cornick 72), Sheehan. Subs - Shea, Justin, Cook, Gambin.
Carlisle United - Bonham, T Miller, Liddle, Hill, Parkes (Etuhu 46), Grainger, Lambe, Jones (Bennett 74), Joyce (Cosgrove 84), Hope, S Miller. Subs - George, Devitt, Brown, O'Sullivan.
Referee - Chris Sarginson
Attendance - 7,644 (215 away fans)