Harwich took the lead when Dylan Crowley (pictured) broke through the visitors' defence to net with a well-taken finish.
Rovers were sitting in second position in the league table and Shrimpers goalkeeper Oscar Finbow was in good form, handling the ball safely and, when called upon, making some good saves.
He was beaten when Stanway equalised with a superbly-taken free kick from 20 yards.
Play was end to end and the teams remained level at half time.
The second half continued to provide excellent entertainment for the appreciative good following of supporters who attended.
With 20 minutes remaining, Harwich were pressing the Rovers defence and were rewarded when Crowley again broke through and deftly placed his shot into the net for the Shrimpers' vital second goal.
Both teams kept up the tempo until the final whistle when it was Harwich who celebrated, taking all three points.