Solihull eased into a 5-0 lead in the opening six minutes but Carlisle then successfully played catch-up, pulling up to 8-5 after two quarters, 8-7 after three and then taking the lead for the first time at 10-8 in the last thanks to goals by Myles Little, Colin Burgess and Sam Routledge.
Tom Whiting's fourth goal narrowed the gap and there were three, tense minutes remaining when Jordan Elliot claimed the final Solihull equaliser.