The Blues eased into a 1-0 lead courtesy of Antonio Rudiger’s first-half goal after Paul Pogba allowed the German defender to escape his attention and fire a header past David De Gea.
Manchester United responded in the second half through Anthony Martial after the France international scored a precise goal to equalise before a placed finish to give the visitors a 2-1 lead.
However, Jose Mourinho’s side couldn’t hold on for his first win at Stamford Bridge after Ross Barkley levelled deep into injury time in west London to preserve their unbeaten start to the season.
Maurizio Sarri’s side have won six times and have drawn three games in their last nine Premier League games to leave the Blues in third place in the table and two points adrift of Manchester City and Liverpool FC.
Chelsea FC struggled in their second season under Antonio Conte and the Italian coach was unable to maintain the team spirit from their title-winning campaign in 2016-17.
Sarri replaced Conte in the summer and the former Napoli manager has cultivated a feel-good atmosphere at Stamford Bridge thanks in part to the attacking brand of football that he is implementing at the Blues.
Luiz, who has forged a strong centre-half partnership with Rudiger in the opening nine games of the season, claimed that the west London outfit proved their togetherness in their 2-2 draw with Manchester United.
“Even though we were 2-1 down, we kept trying to score the equaliser and we did that in the end so I think the spirit was amazing,” Luiz told Chelsea’s website.
“This was a big game against a big club, and it is always like this. We have to realise we had amazing spirit to try and score the second goal and we did that in the end.
“We are happy we have gone this many games without losing, but we are keeping on working hard to try and improve our team because it is just the beginning.
Chelsea FC finished in fifth spot in the Premier League table last season but Sarri looks to have transformed the west London side into title challengers in the current campaign.
The Blues have only dropped points in stalemates with West Ham United, Liverpool FC and Manchester United in the current campaign.
Sarri led Napoli to a second-placed finish in Serie A last season behind champions Juventus.
Chelsea vs BATE Borisov (Thursday 25 October)
Burnley vs Chelsea (Saturday 28 October)
Chelsea vs Derby (Wednesday 31 October)
Chelsea vs Crystal Palace (Sunday 4 November)
BATE Borisov vs Chelsea (Thursday 8 November)
Chelsea vs Everton (Sunday 11 November)
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