Nathan Broadhead scored the only goal of the game in the 10th minute after he was sent through on goal by Corry Evans.
Broadhead was then forced off with an injury before half-time and was replaced by Jack Clarke.
Jay Matete and Dan Neil were also brought on in the second half as Sunderland closed out the win.
Our chief SAFC writer Phil Smith has delivered his verdict on how each Black Cats player fared at the Mazuma Stadium:
1. Anthony Patterson - 6
Comfortable in possession and didn’t have a save to make. 6 Photo: JPI Media
2. Bailey Wright - 7
Dominated his contest with Cole Stockton and was excellent defensively throughout the game. Barely put a foot wrong. 7 Photo: JPI Media
3. Danny Batth - 7
Like Wright was supremely comfortable in the air and rarely troubled. Has become an important player ahead of the play-offs. 7 Photo: JPI Media
4. Luke O’Nien - 6
Moved to the left of a back three and though Morecambe unsurprisingly tried to target that, he came through the challenge and was never troubled too much. Used the ball well enough in a steady display. 6 Photo: Frank Reid