Struggling Town ended the Shrimps' eight-match unbeaten league run with goals from Matt Richards, Terry Gornell and Byron Harrison.
Morecambe skipper Mark Hughes was sent off for a second yellow card early in the second half and Richards also missed a penalty for the hosts.
Yates left skipper Russ Penn and leading scorer Harrison on the bench, but the changes worked as Cheltenham enjoyed their most comfortable win of the season so far.
"We had a scare early on, when Scott Brown made an excellent save, but after that we've controlled the game," Kevan said.
"Whether Morecambe had 10 or 11 players on the pitch we looked comfortable throughout and the goals came at good times.
"The story of the season has been conceding poor goals and scratching our heads about how to eliminate those mistakes.
"The manager deserves so much credit because a lot of managers don't change anything, but he's come up with the answer.
"We had that extra pass, retained the ball better and played more expansively - so he takes the plaudits for that.
"Terry Gornell looked hungry, Sam Deering was bright - as he has been in training - and David Noble really did what he does best, retaining the ball for us so all three players who came in had an impact.
"We passed the ball with a purpose throughout and we didn't take liberties with it, which is important."