Stockport edged closer to the play-off places with first-half goals from Michael Rose and Anthony Elding.
It was their fourth home win in a row - and the fourth game in succession when Elding has been on target.
But manager Jim Gannon admitted that Accrington made it tough for them.
"They are a big, strong side and like to attack," he said.
"We had to defend in the second half, but worked hard and did extremely well. We deserved our clean sheet."