Boss Paul Cook left to join Chesterfield on Thursday and Richardson led Stanley to a first win in five games after four successive defeats.
The clash looked like it would peter out into a goalless draw until, with 11 minutes remaining, Luke Joyce found Rommy Boco on the left and Amond got in front of the visiting defence to fire home his seventh goal of the season and stop the rot for the Reds.
Stanley deserved victory having created the better chances under Richardson, who is favourite for the job on a full-time basis should he not rejoin Cook as assistant at Chesterfield.
Accrington enjoyed the better of the first-half chances as Peter Murphy, Joyce and top scorer Amond all went close.
Rovers were threatening on occasion - Tom Eaves bringing a good saves out of Ian Dunbavin - but it was the hosts who continued to carve out the better opportunities after the break.