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.
Mark Jones was handed the first start of his second United spell, with loanee Conner Robinson having returned to Lincoln City.
Chances were at a premium throughout, although Solihull did boss the early possession stakes and looked a threat through the creativity of Ryan Beswick and the wing play of Darryl Knights.
Vince had to be alert to tip Beswick's angled drive behind before a fabulous block from Greg Tempest denied Bogle after Dayle Southwell and Rene Steer had been heroically denied at the other end by blocks.
Moors took the lead on 27 minutes. BOGLE shrugged off Carl Piergianni to advance goalwards, only to be denied initially by Scott Garner's excellent tackle, but stabbed in the rebound past the wrong-footed Vince.
There was a great chance for the Pilgrims to equalise moments later but Piergianni headed wide following Tempest's deep corner.
United's leveller did arrive four minutes before the break when MILLS let fly from distance and his drive nestled beyond Breeden via a significant deflection off full-back Jordan Gough.
Steer then lobbed wide on the stroke of half-time as the Pilgrims threatened to go into the break in front.
There was a big chance for veteran Solihull frontman Darren Byfield after half-time and his close-range shot hit the post before flying behind off Vince.
The game's defining moment unfolded with 11 minutes to play. Despite initialling allowing play to continue, referee Anthony Tankard heeded his assistant's signal for a Solihull free-kick which was delivered by Gough, spilled by Vince and tapped home by a gleeful ELVINS.
Boston (4-4-2): Sam Vince; Liam Marrs, Scott Garner, Carl Piergianni, Greg Tempest; Zak Mills, Conor Marshall, Michael Hollingsworth (Kyle Dixon 70), Rene Steer (Kaine Felix 82); Dayle Southwell, Mark Jones (Marc Newsham 75). Subs (not used): Stefan Galinski, Niall Doran.
Solihull (4-4-2): Tony Breeden; Michael Nottingham, Liam Daly, Rob Elvins, Jordan Gough; Junior English, Jay Denny, Ryan Beswick, Darryl Knights; Darren Byfield (Owen Story 89), Omar Bogle. Subs (not used): Reece Fleet, Richard Taundry, Keenah Rosser, Darren Acton (gk).
Referee: Anthony Tankard.
Attendance: 883 (15 visitors).
PIC: Tim Hoff.