Ryan Beswick and Akwasi Asante both grabbed a brace as Trinity could not get to grips with the table toppers.
A Liam Davis bicycle kick just after the hour threatened a comeback for the Blues, who had started the second half with a real attacking intent.
That fightback lasted only four minutes as Solihull ran away with it in the end.
Gainsborough began the day by making two changes to the side which secured all three points away at Hednesford.
An injury to Jonathan D’Laryea meant that Charlie Binns started in the centre of midfield, whilst Liam Davis came in on the wing for Courtney Wildin who’s loan move from Sheffield Wednesday ended after the Hednesford game.
Despite the result, the Blues began brightly against the league leaders, going toe to toe with them until the opening goal.
There had been a brief warning from the Moors, with striker Andy Brown heading onto the roof of the net in the 14th minute.
Trinity had a couple shots blocked before Craig Reid had to come off in the 18th minute with a hamstring injury.
Solihull right back Michael Nottingham was causing problems down the Trinity left hand side and his dangerous cross was met by the flying Jake Picton, who turned the ball into his own net.
The visitors became rampant after this and when Stephen Brogan’s pass back was too short, Brown nipped in before Jan Budtz and the big Dane brought him down for a penalty.
Ryan Beswick dispatched the spot kick, sending Budtz the wrong way.
On the cusp of half time, the Moors grabbed a third as Beswick doubled his tally, heading home a Connor Franklyn cross via the underside of the bar.
There could have been a fourth in first half injury time but a sliding Jimmy Armson could not make contact with a cross with the goal at his mercy.
The Blues began the second half on the front foot as they tried to pull off an almighty comeback.
First Jarman hit a venomous strike narrowly over before Picton met a Brogan free kick to force Danny Lewis into a save.
Darryn Stamp and Nathan Jarman both had further opportunities to score before the hour but miscued at the vital moment.
In the 63rd minute, Trinity did manage to get a goal as Liam Davis acrobatically finished off a Stamp chest down from 12 yards out to give some hope to the Northolme faithful.
The hope lasted four minutes though as Gainsborough’s set piece vulnerabilities were shown up by Liam Daly who headed home form a corner at the far post.
It was then Jarman’s term to try out the gymnastics with a scissor kick that looked destined for the net but for Lewis to push it away.
Solihull substitute Akwasi Asante extended the Moors lead on 80 minutes when he beat Budtz to a long ball and rolled into an empty net.
The sub added a sixth in the final minute when he lashed home from the edge of the box.
Gainsborough Trinity: Budtz, Roma, Lacey, Brogan, Davis, Picton, Russell, Binns, Reid (Stamp 18), Jarman, Yates (Karkach 72). Subs (not used): Quinn, Hedge.
Solihull Moors: Lewis, Nottingham, Franklyn, Daly, Streete, Dean, Armson (Walker 45), Byrne, Brown (Asante 69), Beswick (Byfield 82), Knights. Subs (not used): Bignot, Gough.
Gainsborough Goalscorers: Davis 63.
Solihull Goalscorers: Picton Own goal 25, Beswick pen 31, 45, Daly 67, Asante 80, 90.
Referee: Mr R Wooton. Assistants: Mr D Whatling, Mr S Packer.