In dreadful conditions but thankfully on the Coles Lane artificial surface, Roms took a 23rd minute lead through Todd Evans.
And they doubled that lead five minutes later through Chad Degville-Cross, only for Club to respond just before the break with Benny Igiehon`s first goal.
Five minutes after the interval Barry Fitzharris made it 3-1 to the hosts but Igiehon pounced again eight minutes later and with less than three minutes remaining, completed his hat-trick to make it 3-3.
However, Luke Keen popped up to win it for Romulus in injury-time and lift them into fifth spot.
Despite the result, a tight division sees Sheffield down in fourteenth spot but only five points behind Roms.
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