England were bowled out for 313 in their second innings, with fast bowler Gabriel taking 5-75 in 21.2 overs - his sixth five-wicket haul in 46 Tests.
The hosts resumed on their overnight 284-8, with all their specialist batsmen dismissed.
Gabriel had tailender Mark Wood edging a cut to wicketkeeper Shane Dowrich on two to leave England 303-9 in good batting conditions beneath sunny blue skies.
Barbados-born fast bowler Jofra Archer drove Gabriel down the ground for four in spectacular style to extend England's lead to 199 runs.
But next ball Archer was out for 23, caught behind after gloving a hook off Gabriel.
England, chasing the game for most of this match, had been recovering well during a fourth-wicket stand of 98 between Zak Crawley, whose 76 was his highest Test score, and stand-in skipper Ben Stokes on Saturday.
But when Stokes, captaining England in the absence of Joe Root, fell to opposing skipper Jason Holder for 48 - the second time in the match he had been dismissed by his rival all-rounder - it sparked a collapse that saw five wickets lost for 30 runs.
This opening match in a three-Test behind closed doors series marks the return of international cricket from the coronavirus lockdown.