Josh Kelly's early penalty for the hosts was cancelled out by Joe Gallagher's goal before Doug Heseltine intercepted to touch-down for Rishies.
Crocs hit back with first half tries from hooker James Cooper and Matthew Beswick, one converted by Gallagher, to go 18-8 up at the break.
Gallagher extended the lead with a penalty while a try for replacement Sembi Navneet put Crocs in control.
Rishworthians finished strongly and Toby Muscat-Baron, another who had a strong game, forced his way over for a second unconverted try but it was too little, too late for the hosts.
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