Summer signing Mark Lynch gave the Millers the lead after just seven minutes with a wonderful, curling effort from the edge of the area which beat Barry Roche high to his right.
Morecambe threatened briefly before the visitors doubled their advantage five minutes before the break when Ryan Taylor finished an excellent move with a low strike.
The home side came back into the game in the second half, threatening on a number of occasions.
Andy Warrington had to save well from Matty Blinkhorn before the Shrimps pulled one back through Neil Wainwright on 77 minutes.
But Lynch was on target again two minutes from time with another quality curling effort.
Any reproduction, publication or redistribution of this material without the written agreement of 365 Media Group is strictly forbidden.