Jim Bentley’s side probably had the better of the chances on show against the league leaders but failed to take them leaving Mullins the hero for the home side with the only goal on 64 minutes.
Max Muller made probably his only mistake of the game when he gave away a cheap free kick down the left and the home side took advantage as Olly Lee swung in a dangerous ball and Mullins got ahead of his marker to head past Barry Roche from eight yards out.
Bentley made four changes to the side that drew 1-1 with Stevenage with Vadaine Oliver absent as his partner was due to give birth, Callum Lang injured and Kevin Ellison and Alex Kenyon placed on the bench.
In came Garry Thompson, Adam McGurk, Aaron Wildig and Andy Fleming and all four made valuable contributions in a good performance.
The goal came at a time when the Shrimps were on top after dominating the start of the second half with Adam McGurk coming close to giving the Shrimps the lead with a shot on the turn that was deflected wide by Mullins before 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 as they counter attacked swiftly.
The first half saw 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 on 43 minutes and right back Jack Stacey twice forced into goal saving clearances from dangerous crosses.
The Shrimps maintained that pressure on the second half but we're unfortunately undone by Mullins's header.
Luton: Stech, Stacey, Mullins, Rea, Potts, O Lee, D'Ath (rep Cornick 65), Berry, Shinnie, Hylton (rep E Lee 8), Collins. Subs not used: Justin, Cook, Mpanzu, Shea, Famewo.
Morecambe: Roche, McGowan (rep Lund 89), Old, Lavelle, Muller, Conlan, Rose, Fleming, Wildig (rep Campbell 69), Thompson, McGurk (rep Ellison 69). Subs not used: Nizic, Kenyon, Winnard, Brough.
Ref: T Kettle