Darlington, depleted by the dismissal of Lee Turnbull when they trailed their Dr Martens League hosts 2-1 midway through the second half, shrugged off the disappointment of seeing their recovery to lead 3-2 ruined so dramatically. They held firm in extra time before prevailing in a penalty shoot-out.
The irony was that the outstanding Dowling sent Solihull's first spot- kick woefully wide. When the part-timers' other marksman, Nicky Cross, blazed his shot over, Darlington seized the initiative.
The Third Division stragglers should have gone ahead in the 13th minute only for Carl Shutt, a striker who has scored everywhere from Old Trafford to the Nou Camp Stadium, to mark his debut at Moorlands by firing wide of an open goal.
The tit-for-tat scoring started in the 43rd minute when Dowling headed in a corner. Forty seconds later, Brian Atkinson put Darlington level from a penalty, but the wily Cross, a semi-finalist with West Brom in 1982, restored the home lead with a 55th-minute header.
Turnbull's banishment for a sly foul on the keeper ought to have been the cue for Solihull to consolidate their advantage. Instead, Paul Robinson's diving header brought Darlington level before Dorner, an Austrian, scored off a post with the stopwatch showing 90 minutes played. Mr Rennie's bizarre timekeeping - 11 min 10 sec over - angered Darlington, but they kept their nerve to earn a second-round trip to Hednesford.
Solihull Borough (3-4-1-2): Phillips; Penny, Byrne, Brogan; Abell, Mitchell, Bradley, Wolsey; Dowling; Beagan (Rowe, 56), Cross. Substitutes not used: Woodley, Begley, Randall, Adey (gk).
Darlington (4-4-2): Preece; Shaw, Crosby, Devos, Barnard (Turnbull, 56); Shutt (Resch, 58), Oliver, Atkinson, Naylor; Robinson, Dorner. Substitutes not used: Brumwell, Gray, Pataconstaninou (gk).
Referee: U Rennie (Sheffield).