James Beattie's side opened the scoring in the fifth minute when a pass over the top found James Gray. He drew out goalkeeper Barry Roche and set up Lee Molyneux who had the easy task of rolling the ball into the empty net.
It was two after 11 minutes when Kal Naismith slotted home a penalty following a push on Will Hatfield by Kevin Ellison inside the area.
Roche denied Gray the third from a long-range effort as Stanley bossed proceedings.
Morecambe manager Jim Bentley had some stern words for his players at half-time and his side came out with more fire. Jack Redshaw charged clean through but keeper Marcus Bettinelli denied him with his legs.
However, it was Stanley who made the next chance count after 59 minutes when a Hatfield corner was headed against the crossbar by Peter Murphy and the ball bounced out with Dean Winnard stooping to convert from close range.
Number four soon followed when a Molyneux corner was headed home by defender Tom Aldred with 65 minutes on the clock.
Molyneux hit the bar with a long range effort before Morecambe grabbed a consolation goal when Padraig Amond bundled the ball home from a corner with six minutes remaining.
But Stanley had the final say when Molyneux stroked the ball past Roche from 15 yards out in injury time.