Nahki Wells came off the bench in the 69th minute, but Carlton Morris came off the bench to compound more misery on Bristol City, whose poor run of form continues.
Morris struck from close range in the 67th minute after a corner caused a goalmouth scramble which Bristol City was unable to clear.
Justin Donawa came off the bench in the second half, but he and his Solihull could not find a goal in a 0 – 0 draw with Weymouth.
Jonte Smith and his Woking teammates defeated Barnet 2 – 0 on the road in their Vanarama National League match.
Jamar Loza gave Woking the lead in the 28th minute, and then Moussa Diarra doubled the lead in the 68th minute for the win.