Both sides had good chances, but it was the home side who deserved the spoils after peppering the Harriers goalmouth, particularly in the second half.
Harriers started the brighter and had their first chance in the first minute. Some sleepy defending saw Taiwo Atieno shoot wide when he should have done better, before the home side sprung to life.
Mullin had a powerful header well saved by Harriers keeper Daniel Lewis
At the other end Simon Heslop had a shot saved by opposing keeper Robert Elliot, while Marc Pugh fired over in the eighth minute as a flurry of chances came in the opening exchanges.
But Roberts gave Accrington the advantage when he fired past Lewis in the 13th minute.
It was nearly 2-0 two minutes later when Romauld Boco had a shot saved.
Pugh went close to equalising midway through the half but his shot was saved, while David Brown had a good chance for Accrington, but his effort was blocked.
In the 32nd minute Boco fired over and Mullin had a shot turned around the post two minutes later as the home side looked to doubled their advantage. That was the way it stayed until half-time before Kidderminster made one ime as they looked to level following the resumption.
Five minutes into the second half Brown fired wide, and then two minutes later shot wide again.
Harriers saw Michael Blackwood fire wide in the 54th minute with the game finely balanced, before Russell Penn also went close for the visitors.
In the 72nd minute Mullin headed wide and five minutes later Boco shot over. But a minute later Stanley's second goal finally came. Mullin was the scorer as produced a powerful drive which was too good for Lewis.
Lee Thompson nearly reduced the deficit immediately, but his shot a minute later missed the target.
Accrington then held their nerve, kept possession and made sure of the points.