Chris Coyne, Steve Howard and Kevin Nicholls hit the goals in a comfortable victory that saw the hosts spurn a string of opportunities to add to their tally.
Town began with purpose and Nicholls' dangerous fourth-minute cross almost picked out the onrushing Howard at the far-post, but the ball just eluded the prolific frontman.
County's first effort came with a flash tenth-minute free-kick routine that saw Darrell Clarke flick the ball up for Rickie Lambert to volley wide from 25 yards out.
Howard and Coyne both put efforts over the bar before Luton took the lead in the 28th minute.
Steve Robinson's in-swinging corner fell for both Curtis Davies and Nicholls to have efforts hacked off the line before Coyne swept home from ten yards for his third goal of the season.
Davies came close again eight minutes later when he saw his header after another Robinson corner pushed over the bar by Neil Cutler and Howard then volleyed wide when given time in the penalty area following Kevin Foley's 37th minute pass.
Rowan Vine missed a great chance to make it 2-0 in the 40th minute when he ran clean through from Ahmet Brkovic's flick, but shot timidly wide with just Cutler to beat.
The miss almost proved costly immediately as Warren Feeney beat Alan Neilson and Coyne and saw his cross fall to Damien Allen, whose 15-yard effort was kicked off the line by Nicholls.
The ball came straight back in and Jon Daly headed just wide from eight yards.
Stockport started the second-half brightly, but it was Luton who stretched their lead in the 54th minute when Brkovic found space on the right and crossed for Howard to poke home his 18th goal of the season from close range.
Nicholls banged home number three from the penalty spot in the 74th minute after County skipper Jim Goodwin handled in the area.
Stockport substitute Danny Jackman almost pulled one back after running clean through from Feeney's pass, but saw Marlon Beresford superbly block his effort.