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Mount finished superbly in the first half to seal a 1-0 win and extend the Blues' unbeaten run to 10 matches under Thomas Tuchel, who came out on top in the battle of the two former Borussia Dortmund bosses.
Jurgen Klopp's Reds are four points adrift of the London club in seventh place after suffering yet another loss at Anfield, where they are without a win in seven matches.
The struggling champions were toothless and Mohamed Salah was not impressed when he was replaced by the fit-again Diogo Jota as they suffered yet more misery on Merseyside.
Timo Werner rifled into The Kop and wasted a better chance from close range on the half-volley in a lively start from Chelsea following a minute's applause for Liverpool great Ian St John, who died on Monday at the age of 82.
The Germany forward found the back of the net after racing past Reds goalkeeper Alisson - playing for the first since the tragic death of his father - midway through the first half but was adjudged to be marginally offside.
Sadio Mane missed his kick when he had a clear opportunity to put Liverpool in front and it was Chelsea who opened the scoring three minutes before half-time through Mount.
The England midfielder took a pinpoint pass from N'Golo Kante and was allowed to cut inside by Fabinho, starting after recovering from injury, before picking his spot in the far corner of the net from inside the penalty area with a clinical finish.
Kante was relieved when the VAR verdict was no penalty after Roberto Firmino's cross struck the midfielder's arm early in the second half.
Andy Robertson cleared Hakim Ziyech's effort off the line and a disgruntled Salah came off shaking his head 62 minutes in when he was replaced by Jota, making his first appearance since suffering a knee injury in December.
Rock-solid Chelsea comfortably saw out an impressive victory, with Ozan Kabak prevented from scrambling in a late equaliser as the Reds endured another hugely frustrating evening in which they once again lacked a cutting edge.