Town took the lead in the Southern Combination League Division 2 match through Ollie Finney after 14 minutes and that was how things stayed until half-time.
Rob Clark made it 2-0 five minutes into the second half, before Charlie Romain got the third just past the hour.
Storrington got a goal back through Matt Searle ten minutes from time but their nine-game unbeaten run came to an end.
Town manager Gerry Murphy was pleased to bring a run of three consecutive draws to an end.
He said: “It was nice to play well at home, in front of a good crowd, against a good organised team. Moving up to third keeps us in shape for what will be a tough January.
“The game was pretty much over by the hour, but to Storrington’s credit they battled hard and scored a deserved goal.”
The win increased Steyning’s unbeaten run to five games and moved them above Mile Oak and up to third in the table. They trail second-placed Saltdean by three points and leaders Lingfield by six points but have played a game more than than the top two.
Town host Billingshurst on Monday (11am).
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