Padraig Amond’s 79th-minute goal gave Richardson all three points as he took temporary charge for the first time since Cook’s exit to Chesterfield. He is set to be offered the job on a permanent basis.
Both goalkeepers did well to keep the score at 0-0 until late in the game.
Bristol Rovers keeper Neil Etheridge twice denied Amond with good saves, while Rommy Boco put a free header wide when presented with a golden opportunity from Lee Molyneux’s corner.
Etheridge also kept out another effort from Boco, this time from 20 yards, while Ian Dunbavin twice had to deny Tom Eaves at the other end.
Amond broke the deadlock with 11 minutes left, though, as he turned home Boco’s right-wing cross from close range.
Stanley handed a debut to substitute Osayamen Osawe, who has joined the Reds on loan from Blackburn Rovers.
Stanley: Ian Dunbavin; Dean Winnard, Peter Murphy, Rob Atkinson, Michael Liddle; Luke Joyce, George Miller; Rommy Boco, Will Hatfield (Osayamen Osawe 59), Lee Molyneux (Bohan Dixon 90); Padraig Amond (Jack Sampson 90). Subs not used: Andrew Dawber, Toto Nsiala, Craig Lindfield, Piero Mingoia.
Bristol Rovers: Neil Etheridge; Matt Lund, Gary Kenneth, Jim Paterson, Lee Brown; Wayne Brown, David Clarkson, Oliver Norburn (Derek Riordan 59), Fabian Broghammer (Joe Anyinsah 77); Tom Eaves, Eliot Richards. Subs not used: Sam Walker, Ellis Harrison, Ollie Clarke, Seanan Clucas, Tom Lockyer.
Referee: Robert Lewis.