Visiting skipper Rob Elvins struck the winning goal on 79 minutes after Rene Steer had been wrongly penalised for an apparent handball and keeper Sam Vince dropped the resulting Jordan Gough free-kick.
Zak Mills had earlier cancelled out Omar Bogle's opener for Solihull and the match appeared to be heading for a draw until Moors' moment of fortune.
PIC: Tim Hoff.