Arsenal, meanwhile, end a miserable defensive record at the Bridge.
Luiz could have been sent off earlier when he attempted a dramatic overhead strike on goal only to leave Arseneal defender Laurent Koscielny needing treatment.
But will the Blues be too much for Arsene Wenger's men, who have had a tumultuous start to the Premier League campaign?
The England forward's return to form had been one of the big positives for Arsenal so far this season but, after missing one excellent first-half chance, he was clearly in some pain when he left the pitch during the second half.
In doing so, the visitors were able to get in behind N'Golo Kante and Cesc Fabregas on a regular basis.
They should have taken the lead just before half-time when Ramsey had only Courtois to beat after weaving his way past Cesar Azpilicueta and David Luiz.
Chelsea continued to lack a cutting edge after the break and Willian shot straight at Cech, then blazed over from long range as another attack petered out.
A disappointing Chelsea display ended on a sour note when Luiz followed through recklessly on Kolasinac and referee Michael Oliver reached for his red card. He was immediately shown a red card by referee Michael Oliver.