Goals from Alex Whittle and Akwasi Asante put Town ahead after 20 minutes in Paul Cook’s first home game in front of more than 7,000 at the Technique Stadium.
But the turning point came just two minutes later when captain Curtis Weston was shown a straight red card for an off-the-ball incident involving Solihull’s Mark Ellis, who was booed for the rest of the match by the home fans.
Moors pulled a goal back before half-time when James Clarke headed in a deep cross from Harry Boyes.
And two quick-fire goals after the break from Callum Maycock and Boyes turned the game on its head.
The day went from bad to worse for the hosts when Jak McCourt was stretchered off late on, with no action taken by referee Smith for the strong challenge on the midfielder.
Chesterfield fans vented their anger at Smith throughout the game and he was jeered off the pitch after the full-time whistle.
The DT received confirmation at 5.30pm that there would be no post-match interviews from the Spireites camp.
The decision not to speak to the media is believed to have made to avoid any potential fines or punishment for speaking out against Smith.
The defeat leaves Town still second in the National League, but they are now six points behind leaders Stockport County, who beat Woking 1-0 despite having a man sent off.
Today’s loss was Chesterfield’s first on home turf this season.
They are next in action on Tuesday night against seventh-placed Wrexham.