Hatters skipper Johnny Mullins was the hero for the home side with the only goal of the game in the 64th minute.
Max Muller made probably his only mistake of the game when he gave away a cheap free-kick down the left-hand side.
And the home side took advantage as Olly Lee swung in a dangerous ball and Mullins got ahead of his marker to head past Shrimps keeper Barry Roche from eight yards out.
The goal came at a time when Morecambe were on top after dominating the start of the second half.
Adam McGurk came close to giving the Shrimps the lead with a shot on the turn that was deflected wide by Mullins.
Then the same Morecambe player went close again with a flick that forced a fine save from Marek Stech at full stretch.
After the goal the Shrimps continued to cause the Luton defence problems with substitute Kevin Ellison denied a clear run on goal by Glen Rea’s last-ditch tackle, before the Shrimps’ veteran went close with a drive from the edge of the area.
Luton had their own moments with substitute Harry Cornick twice forcing Roche into decent saves.
The first half had seen Luton control much of the possession.
But it was the Shrimps who looked the more threatening, with Aaron McGowan forcing Stech into an excellent save in the 43rd minute.
And right-back Jack Stacey was twice forced into goal-saving clearances from dangerous crosses.
The Shrimps maintained that pressure in the second half and put Luton under sustained pressure but were unfortunately undone by Mullins’ header.
Luton Town: Stech, Stacey, Mullins, Rea, Potts, O Lee, D’Ath (Cornick 65), Berry, Shinnie, Hylton (E Lee 8), Collins.
Subs (not used): Justin, Cook, Mpanzu, Shea, Famewo.
Morecambe: Roche, McGowan (Lund 89), Old, Lavelle, Muller, Conlan, Rose, Fleming, Wildig (Campbell 69), Thompson, McGurk (Ellison 69).
Subs (not used): Nizic, Kenyon, Winnard, Brough.
Referee: T Kettle.