Wanderers trailed 8-4 towards the end of the second period but recovered to trail 10-8 at the end of the third - and then draw level at 10-10 with goals by Joe Jenkins-Delf and Matt Griffiths.
As excitement mounted, the game went to 11-11, then 12-12, before Oliver Vodden netted the winner from a man-up chance 2.14 from the end. Jake Vincent scored four of the Solihull goals.
Later, Manchester won again - 17-8 against Polytechnic, including a seven-goal haul for Dan Paddon. Then Cheltenham eased to a 16-5 victory over Lancaster.
Photo (Trevor Hyde): Cheltenham's Jake Polster, white cap, takes on Jacob Darlington, of Lancaster.
Chris Taylor and Matt Veale both scored six times as Newport outplayed Tyldesley 20-11 in Division 4. The Army raced into a 6-0 lead against Bridgefield and eventually won 16-12.
In Division 5, Coventry and Caledonia Storm drew 15-15, Coventry levelling for the last time when Rob Williams scored his fifth goal.