The Blues were on course to move level on points with leaders Manchester City when Eden Hazard raced clear to score his second goal of the week against the Reds.
Mohamed Salah and Roberto Firmino had shots cleared off the line as Liverpool - who started the game second in the table - pressed for an equaliser, and Hazard was denied by Allison at the other end.
But, as the clock ticked down, Sturridge had the final say - bending a beautiful strike into the top corner from 30 yards.
The draw ended Liverpool's 100% start to the Premier League season - and they finished the day behind defending champions Manchester City on goal difference. Chelsea are two points back in third.
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