The Shots task was made easier when the Shrimps were reduced to ten men, goalkeeper Ryan Robinson was shown a straight red card for handing outside of his area.
Despite being a man light however, Morecambe were poor all afternoon and unable to produce anything of substance sufficient enough to worry Shots stopper Nikki Bull.
Aldershot took an early lead with on-loan striker Dixon netting his third of the season. Barely four minutes had elapsed when the Shots worked Darren Barnard's throw to Ryan Williams. Williams took his time and then delivered a pinpoint cross to the head of Dixon who powerfully headed in unopposed.
Robinson's first action of the afternoon was to gather the ball from his net, and then Morecambe's number one's afternoon came to an early end when he accidentally handled outside of his area, attempting to halt Griffiths latching onto Steve Watson's raking pass.
A clear goalscoring opportunity was denied and as he was the last line of defence Robinson was shown a straight red.
As the Shrimps tried to re-group, the Shots almost doubled their advantage on 16 minutes, through Barnard's 20-yard drive, which substitute goalkeeper Steven Drench did well to save.
Midway through the first half Drench prevented the Shots going further ahead, saving Nick Crittenden's low strike down to his left, and then two minutes before the break, Griffiths' low header from Williams' cross from the left flashed just wide of Drench's upright.
Griffiths however was not made to wait too long for his third goal for the Shots, two minutes into the second half in fact.
The marauding frontman looped his header from Watson's cross and this time Drench was beaten.
Aldershot's dominance should have been further rewarded, but Tobi Jinadu saw his header cleared off the line, with Williams' late screamer flashing just wide.