In the second half, the game became fractured, with just fractions coming between a Liverpool equaliser and a two-goal Chelsea lead, Xherdan Shaqiri and Hazard both coming within inches of scoring for their respective sides.
Unless he has a season like Cristiano Ronaldo enjoyed in his penultimate one at Manchester United in 2007-08, when the Portuguese scored 42 goals in all competitions, Hazard will need help from elsewhere if Chelsea are to have a realistic chance of winning the league.
Liverpool will be thrilled to have avoided defeat, especially given the games to come next week: a trip to Napoli in the Champions League, and a showdown with City at Anfield.
Next Alisson was beaten with a move Hazard started and finished.
N'Golo Kante (8/10): Kante played a vital role in the Chelsea midfield as he not only screened the defence with his brilliant ball-recovering qualities but he also created a lot of chances for the attackers with his quick thinking.
Arsenal legend, Ian Wright, has predicted the scoreline of the Premier League game between Chelsea and Liverpool on Saturday.
There's still a lot of time left for somebody to beat this goal, but for now, it's the best we've seen in the Premier League this season.
"It's important for every club to try to pick up points and these games are important, but even if you drop points in these games it's about having the consistency throughout the whole season because this is just one game in 38 anyway".
Liverpool's most recent title success came in 1989-90 and Chelsea supporters reminded the visitors of recent near misses, singing about Steven Gerrard's slip in April 2014 which effectively ended the Reds' title challenge. "Gini (apart from that back pass ) was also brilliant I think".
And up next for Sarri's men in the Premier League is a trip down to the south coast to play Southampton next Sunday (2.15pm).