Israel international Solomon, who played under De Zerbi at Shakhtar Donetsk, struck two minutes from time at the Amex Stadium after Albion had dominated.
Solly March and Facundo Buonanotte had goals disallowed for the Seagulls, who failed to score in the top flight for the first time since October, despite registering 21 attempts.
Fulham, without star striker Aleksandar Mitrovic due to a minor injury, struggled for a foothold in the game for the majority of the afternoon before the late twist boosted their hopes of European qualification at the expense of their hosts.
Loanee Solomon’s second goal in as many matches moves Marco Silva’s men above Brighton into sixth spot, albeit they have played two games more.
De Zerbi, who berated referee Darren England following the final whistle, had spoken candidly of his desire to bring continental football to Sussex on the back of taking 20 points from the last 30 available.
His in-form side began with purpose and intent as they controlled proceedings against top-half rivals missing their main source of goals.
Evan Ferguson lashed over and March curled wide early on, while Joel Veltman’s powerful attempt at the end of a well-worked free-kick routine was later blocked by Tim Ream.
Fulham offered almost nothing from an attacking perspective but continued to defend doggedly, although they often looked susceptible to being carved open by the Seagulls’ slick interplay.
Cottagers goalkeeper Bernd Leno had to be alert to smother the ball as Ferguson burst through on goal and was then well-positioned to stop Alexis Mac Allister’s stinging volley.
The pattern of play, with Brighton patiently probing as the visitors sat back, persisted into the second period.
Seagulls captain Lewis Dunk headed narrowly off target from an out-swinging March corner before the hosts, who suffered VAR frustration in last weekend’s 1-1 at Crystal Palace when Pervis Etupinan incorrectly had a goal ruled out for offside, called for Stockley Park intervention to aid a penalty appeal.
Veltman tumbled in the box under a challenge from Antonee Robinson following Kaoru Mitoma’s low cross but, after Leno denied March from the loose ball, match official England stuck with his decision to award a corner.
With the perceived injustice firing up the home crowd, Albion continued to push forward in search of a breakthrough.
March poked home at the back post after Adam Webster nodded on a Pascal Gross corner but was clearly offside before Leno produced a fine reflex stop to deny Mac Allister’s close-range volley.
Fulham’s top-flight scoring statistics suggest an over-reliance on the absent Mitrovic.
Four-goal Bobby De Cordova-Reid was their leading scorer on show on the south coast and he threatened with a blocked attempt during a rare burst forward.
But the one-way traffic was largely unrelenting.
Brighton were denied by a flag for a second time in the 77th minute due to Deniz Undav being marginally offside before squaring for fellow substitute Buonanotte to slot in.
German forward Undav – still seeking his first goal in English football – then threatened with two quick-fire headers, a glancing effort which flashed wide following a tame close-range attempt.
Albion had never beaten Fulham in the top flight and that run continued following the painful sucker-punch.
After a Seagulls attack broke down, Solomon was released by fellow replacement Carlos Vinicius before expertly steering a low effort into the right corner.