Sarri has spoken highly of Alonso on several occasions this season and relied upon the 27-year-old so heavily that January signing and Italy worldwide Emerson Palmieri has been limited to just two appearances in all competitions.
But Sarri can no longer afford to ignore Loftus-Cheek, not on this evidence.
The second score happened six minutes later, with the England global barely beating teammate Olivier Giroud for a close-range tap-in in front of the net.
He was also understood to be a target for several clubs around Europe this season.
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Pedro curled a deflected shot agonisingly wide and Mateo Kovacic - one of three Chelsea players to retain their spot in the side from Saturday's 2-2 draw with Manchester United - prodded wide from closer range as he attempted to join Loftus-Cheek in getting off the mark for the season. But by then it was too little, too late.
Sarri has come in and transformed Chelsea, who are undefeated in 12 games in all competition, and the switch in formation to 4-3-3 has seen Moses lose his place, with the club's good form hindering opportunities for reserve players. Callum Hudson-Odoi is on the bench and will be hoping to make his European debut for Chelsea against BATE Borisov.
It was a night that will never be forgotten by the 22-year-old as he scored his first career hat-trick for the west London club.
With a victory seemingly assured, Chelsea let off the gas pedal and allowed BATE to create some chances in the later stages of the match.
"I know it's against BATE Borisov and they're not the best, but I think if he can do this, if he can add goals to his game, and take up a position in the side, I think he's got all the talent in the world".