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Van Dijk rose high above his marker to head a corner back across goal and into the far corner in the 118th minute.
Liverpool's patched-up side came out after the break in top gear.
City tested Chelsea's back line with 31 shots to the visitors' nine, but only five were on target.
Liverpool moved five points clear atop the Premier League to set up a potential thriller on Sunday against third-placed Arsenal.
Uruguayan Nunez put the seal on a dominant Liverpool display with his second goal in stoppage time.
Ten-man Chelsea beat Brighton & Hove Albion 3-2 at Stamford Bridge while fourth-placed Aston Villa needed a late Ollie Watkins goal to scrape a 2-2 draw at Bournemouth.
Gareth Southgate's 26-man squad for Qatar was announced Thursday.
Chelsea completed the double over AC Milan to top Champions League Group E with a 2-0 victory at San Siro on Tuesday.
Arsenal posted a 3-1 win over 10-man Tottenham at the Emirates Stadium.
Real Madrid’s chances of defending its crown probably depend largely on having a fully fit Benzema.