Roberto Firmino saw a header hooked off the line by David Luiz as the visitors kept Chelsea pinned back, before Sturridge rescued a result with a curling strike from almost 30 yards out that left Kepa with no chance.
Chelsea is two points behind City and Liverpool in third place.
"Focussed and looking forward to another big game tomorrow against Chelsea at Stamford Bridge", the 27-year-old wrote on Friday.
"He's fantastic football player, he had a full preseason and he's in the best shape since I've known him".
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"Hazard has got this energy about him at the moment, a zip, that confidence".
"Hazard is always thinking, always on the move, really hard to play against". He was taken off for Shaqiri with 24 minutes left.
Hazard's sublime first-half opener at Stamford Bridge - his seventh goal of the season - looked like giving the Blues another victory over Liverpool three days after the Belgian's Carabao Cup victor at Anfield.
Liverpool missed a number of chances to level things up and it looked like they were going to taste defeat for the first time in the Premier League this season with the ninety minutes nearly up.
However, it was another substitute, Daniel Sturridge, who made the difference by finding the equaliser with a stunning curling effort from distance in the 88th minute.
Prior to being replaced 55 minutes into Liverpool's sixth straight league win, Van Dijk had played every minute of the 2018-19 campaign.
Marcus Rashford came off the bench to briefly give United hope by pulling a goal back, but just three minutes later Marko Arnautovic exposed more poor United defending to seal West Ham's first home league win of the season.
"Top managers make players believe in what they are doing".