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.
West Ham barely had time to process what had happened, before inexplicably conceding another.
There have been occasions when West Ham have been genuinely awful under Bilic. West Ham boast neither the technical quality nor the right system to genuinely outplay Liverpool in midfield, but in those two situations, nearly outside the overall tactical battle, they might have caused problems. What Liverpool surely required was someone who could drop off, create three-against-two situations in midfield to bypass Noble and Pedro Obiang.
The first goal left beleaguered boss Bilic furious as it came from a West Ham corner.
While he isn't the most prolific front man in the Premier League, his hard-working attitude and skill on the ball makes him stand out to the Reds' supporters.
Suprisingly from kick-off, Liverpool restored their two-goal advantage in the 56th minute when Alex Oxlade-Chamberlain bundled in his rebound into the roof of the net for his first league goal for Liverpool.
Liverpool put the game beyond the Hammers in the 75th minute after Salah was picked out by Mane.
However, hope for West Ham lasted just 55 seconds.
A 4-1 thrashing at the hands of Liverpool seems to have been the final straw for the club and Bilic, with the Hammers sitting just above the relegation zone heading into the global break.
West Ham got back into the game 10 minutes after the break.
"I had the confidence to come to England again, I am not surprised", said Salah when he was asked post-match if he could have imagined his start to life in a red shirt would go so well.