Rawcliffe led twice through neat finishes from Ricky Hunter, but were pegged back by the hosts on both occasions.
Andy Kirkham levelled the first time, before Chris Jackson equalised a second time from the penalty spot.
With barely a minute remaining, Jackson broke through the Rawcliffe back line to hit the winner for Cliffe, who have games in hand on the leading sides.
Division three’s Crayke led nine-man Acorn 2-1 at half-time thanks to goals from Mark Aconley and Karl Slater.
Aconley added three more in the second half and Slater a second to give Crayke a welcome 6-1 win.
Tom Knowles (2), Josh Knowles and Jed Vale found the mark for Bishop Wilton as they inflicted a 4-0 defeat on Civil Service.
In the Supplementary Cup, two goals from Mikey Brown were not enough to secure victory for Brooklyn as they went down 3-2 to Tadcaster Magnets.
Sam Harrison (2) and George Phillipson picked up Magnets’ haul.