Defender Liam Kitching’s second goal in three gave Simon Weaver’s side a seventh-minute advantage, and although the visitors hit back almost immediately, second-half finishes from George Thomson and Callum Howe sealed a 3-1 success.
Despite the Midlands outfit being a team full of giants, it was Town’s Dominic Knowles who rose highest to nod Joe Leesley’s early left-wing corner goalwards, and Kitching was on hand to add a finishing touch from close range.
The home lead was however short-lived and just four minutes later Adi Yussuf pulled Moors level.
Jamie Reckord’s cross was helped on to the Solihull number nine and he had time to take a touch before smashing a strike from six yards out that just about found its way through Harrogate keeper James Belshaw and over the line.
Less than 60 seconds after conceding, Town almost had a second when Kelvin Lagmead got on the end of central defensive partner Howe’s pull-back, but saw his effort blocked.
Former West Bromwich Albion and Birmingham City midfielder Darren Carter then planted a 25-yard free-kick just the wrong side of Belshaw’s left-hand upright, and as the end-to-end nature of the contest continued, both sides launched threatening raids without managing to create anything clear-cut.
After a fairly even opening 35 minutes it was Town who finished the half the stronger and Moors were forced to do some defending as their hosts enjoyed a decent spell of pressure just before the break.
Josh Falkingham drilled one from the edge of the area, but the shot was too close to Ryan Boot in the away goal, then Warren Burrell’s blast was blocked by a defender.
The second period was only four minutes old when Weaver’s men went close again, Langmead’s header from another inviting Leesley corner-kick being cleared off the line and then striking Jack Muldoon who diverted the ball onto the outside of the post and behind.
What followed wasn’t anywhere near as fluid as the first 45 minutes, but after a fairly uneventful period of play, Town scored two goals in quick succession for the third match in a row.
With a quarter of an hour remaining, Leesley won the ball in middle of the pitch and spotted the run of Thomson, who cut in from the right and then reversed a low left-footed effort past the despairing dive of Boot.
Three minutes later, Leesley’s right-wing corner was met by Howe, climbing majestically at the back stick to power a header into the top corner and wrapping up the points.
Substitute Mark Beck, returning from an injury lay-off, could have added a fourth eight minutes from time, only to nod into the ground and wide when well-placed, then saw another weak header saved, however Town had already done enough.