The midfielder stepped up to convert from 12 yards for his third of the season, and the hosts were in firm control at the Store First Stadium when McCartan's long-range strike took a deflection and beat Scott Davies.
Accrington would have been three up had Davies not produced a full-length dive to keep out Sean Maguire's header.
Davies denied Maguire again when the three-goal striker curled an effort towards the top corner, but Morecambe also threatened before the break as Mullin and Alex Kenyon forced saves out of Jesse Joronen.
Joronen, who is on loan at Accrington from Fulham, was stretchered off four minutes into the second half with a serious-looking injury, and his replacement was beaten within three minutes of coming on.
Mullin nodded beyond Luke Simpson from inside the six-yard box after a cross from Shaun Beeley as the Shrimps pulled a deserved goal back, with Kevin Ellison and Kenyon having previously gone close since the interval.
After Padraig Amond missed a golden chance to equalise for the visitors, Accrington soon regained control of proceedings and should have restored their two-goal advantage with one of several opportunities.
Lee Molyneux, Marcus Carver, and Maguire were all thwarted by man of the match Davies in the Morecambe goal, but Stanley had already done enough to secure a victory which sends them ninth in the table.