Morecambe couldn't deal with sharp shooter Lee Jones whose three goals virtually settled the game in favour of the league side.
Jones opened the scoring after 37 minutes courtesy of a mistake by Chris Lane who lost the ball close in and the Wrexham striker hit a low shot under Craig Mawson, who got his hands to it but couldn't keep it out.
Morecambe might have equalised soon after when Adriano Rigoglioso crossed from the left but Ryan Sugden missed it near the line and Jamie Murphy mis-kicked at the back post when the slightest touch would have turned it in.
A collision between Iain Swan and Hector Sam after 51 minutes was ruled to be a penalty by referee Eddie Evans, although Morecambe fans thought the Wrexham player had tripped over his marker.
Jones stepped up to convert the spot-kick, sending Mawson the wrong way.
The Red Dragons striker completed his hat-trick after Sam pulled the ball back from the line, and when Sam was brought down again, this time by Murphy who received a red card for his troubles, he took the spot-kick himself to make the score 4-0.
Craig Morgan then turned the ball past his own keeper to give the Shrimps a consolation goal.