Shepherd Murombedzi caught the hosts cold to play in Harry White and the former Barnsley forward made no mistake to fire Solihull in front after nine minutes.
White could have made it comfortable for Solihull just before the break, but he was unable to hit the target after George Carline's neat flick put him through.
Bromley were left frustrated as Brandon Hanlan and Mark Goldberg squandered decent chances.
And Solihull were left clinging on when debutant Daniel Udoh picked up two yellow cards to be sent off with five minutes remaining - just eight minutes after coming off the bench.
Report supplied by the Press Association
Match ends, Bromley 0, Solihull Moors 1.
Second Half ends, Bromley 0, Solihull Moors 1.
Joe Anderson (Bromley) is shown the yellow card for a bad foul.
Jack Byrne (Solihull Moors) is shown the yellow card for a bad foul.
Liam Daly (Solihull Moors) is shown the yellow card for a bad foul.
Substitution, Bromley. Bradley Goldberg replaces Blair Turgott.
Oladapo Afolayan (Solihull Moors) is shown the yellow card for a bad foul.
Substitution, Bromley. Jordan Wynter replaces Lee Minshull.
George Carline (Solihull Moors) is shown the yellow card for a bad foul.
Jordan Higgs (Bromley) is shown the yellow card.
Substitution, Solihull Moors. Oladapo Afolayan replaces Regan Charles-Cook.
Substitution, Bromley. Louis Dennis replaces Connor Dymond.
Second Half begins Bromley 0, Solihull Moors 1.
First Half ends, Bromley 0, Solihull Moors 1.
Goal!  Bromley 0, Solihull Moors 1. Harry White (Solihull Moors).
First Half begins.
Lineups are announced and players are warming up.

The deal for the Long Ashton site made the council look "totally incompetent" and threatened "to turn it into a laughing stock" a Tory councillor said.
John Goulandris said money had been wasted paying the firm Park-and-Ride (PRL) for years after the council was obliged to do so.
The city's transport boss said the subsidy had stopped the service ending.
The site on the outskirts of Bristol was built in 1997 and leased to PRL.
The council subsidised it for the first six years, but after that the service was not profitable and the council ended up running the buses.
Mr Goulandris said: "Local taxpayers will be rightly outraged that we appear to have been paying this company a huge subsidy, amounting to between £5m-£6m, simply on being invoiced for managing the park-and-ride site.
"Whilst I appreciate there is a lot of anguish over the current wholesale review of council expenditure to identify potential savings, this exposé demonstrates that the local authority has been incredibly wasteful - even blasé - over the use of its resources."
Mr Goulandris said there should now be a review "into who agreed such a one-sided bargain".
1,500
parking spaces
£4 adult fare on 903 route (before 1000) to city centre. £3 off-peak and Saturday
£3.70 adult fare on 505 route
Peter Mann,  the council's director of transport, said if it had not continued with the subsidy after 2002 "there would be no park-and-ride", which he described as "critical to the city".
The authority revealed it had been paying the subsidy for 14 years beyond its contractual obligation, during a budget review.
Officers advised an immediate end to the payments which was passed by council.
Mr Mann said the authority was looking to see if it could reduce costs so the service can continue.
"We need to continue the private dialogue with NCP [which owns PRL]... to come to a sensible conclusion."
NCP said while it was in "active dialogue" with the council "it would be inappropriate to comment any further."
But in a In a letter from NCP's solicitors  it said if the council removes the payments "our client would... reconsider the commercial viability of continuing the P&R operation".
Bristol City Council has yet to comment.
Solihull held on to claim a narrow victory over Bromley despite being reduced to 10 men late on.
[NEXT_CONCEPT]
A park-and-ride firm was paid £400,000 a year despite not running any buses since 2010, it has emerged.