Saturday's dismal defeat leaves the Hammers languishing a point and a place above the bottom three and the London Stadium crowd let their feelings be known at both half-time and the final whistle.
Salah opened the scoring in the 21st minute as he and the returning Sadio Mane, making his first start in a month, embarked on a devastating counter from a West Ham corner, 13 seconds elapsing between the taking of the set-piece and the ball nestling in Joe Hart's net.
Joel Matip's first of the season also arrived from a corner, this time in more conventional fashion three minutes later, as the defender converted the rebound after Hart's save from Mark Noble's deflection.
Manuel Lanzini halved the deficit 10 minutes into the second period with a fine finish, but any hopes of a Hammers comeback were effectively snuffed out 55 seconds later as Alex Oxlade-Chamberlain fired home a rebound past the luckless Hart for his first league goal for the Reds.
There was little sympathy for the beleaguered Bilic from Liverpool, who wrapped up a resounding success with Salah's 12th strike of the campaign, lifting Jurgen Klopp's men back above Burnley into sixth.
The in-form Andre Ayew came into this clash with three goals in his past two outings and he almost added to that tally in the ninth minute.
Lanzini's throughball deflected kindly into the path of the Ghanaian, who lifted his effort over the onrushing Simon Mignolet only to be denied by the outside of the post.
To further rub salt into the wound, two corners brought two Liverpool goals in the space of three minutes, the first of which arrived following West Ham's own attacking set-piece.
Salah poked the cleared ball onto Mane, whose searing pace took him away from his toiling chasers, and the Senegalese returned a pass to Salah for a composed finish under Joe Hart.
The Egyptian was involved in the second, too, as his low corner was deflected goalwards by Noble where Hart could only parry back into the danger zone and Matip tapped home.
West Ham thought they were back in it when Lanzini held off the attentions of Joe Gomez to chest down Ayew's cross and loft a calm finish past Mignolet, but with celebratory bubbles still in the east London air, Liverpool were level within 60 seconds.
Roberto Firmino fed Oxlade-Chamberlain, who saw his initial effort well saved by Hart but the winger reacted quickest to smash home his second attempt.
Lanzini was more wasteful as the Hammers sought an equally rapid response, firing over with just Mignolet to beat and Javier Hernandez headed over before Firmino shot wide with Liverpool sensing a killer fourth.
That duly arrived 15 minutes from time as Salah controlled Mane's pass and rifled a left-footed shot into the bottom-right corner, sealing a marvellous outing for Liverpool and a devastating one for Bilic and West Ham.
