The Brazilian centre-back was given his marching orders in the 86th minute for a two-footed lunge on Sead Kolasinac but it was too late for Arsenal to claim a first victory away to the champions since 2011.
Though Arsenal were much improved from their 4-0 drubbing at Liverpool they perhaps benefitted from a Chelsea side lacking the star power of Eden Hazard in attack as Alvaro Morata struggled to impose himself on a disciplined visiting defence.
Whilst Arsene Wenger was without Mesut Ozil (knee) and Alexis Sanchez (match fitness), Antonio Conte chose not to unleash Hazard from the start.
Undoubtedly the Blues were worse off without his ability to drive through the space between the lines but in the early exchanges they were at least aided by the absence of an Arsenal midfield.
Time and time again Arsenal’s back five found themselves man-to-man with the Chelsea attack, leading to Willian finding space on the edge of the box to curl an effort straight at Petr Cech.
Arsenal enjoyed a flurry of pressure down the right, with Danny Welbeck and Alexandre Lacazette going close within the space of a few seconds from Hector Bellerin crosses.
But the lack of protection for Arsenal’s midfield threatened to cost them when Cesc Fabregas, who struggled to impose himself on proceedings, unleashed Pedro with a ball over the top. The Spanish forward should have done better than to volley straight at Cech.
Further forward the midfielders were making chances of their own, Xhaka firing a 25-yard drive wide to the right. Perhaps the best chance of the half fell to Ramsey, whose stumbling run took him past three Chelsea defenders before he toe-poked an effort against Thibaut Courtois’ left-post.
Though they weren’t always adequately protected Arsenal’s defence were taking all Chelsea could throw at them, even a boot from Luiz into Laurent Koscielny’s face seven minutes into the second half.
Similarly Arsenal’s intricate attacks all too often found a roadblock before they could test Courtois. Inevitably both managers would need to turn to their superstars on the bench, with Lacazette making way for Sanchez on 66 minutes. Three stoppages of play later Hazard entered the fray, Willian making way as the phoney war came to an end.
Hazard soon brought a good save out of Cech but it Arsenal, who also introduced Olivier Giroud after a worrying injury for Danny Welbeck, went on the front foot and had the ball in the net when Mustafi flicked home Xhaka’s free-kick only to see it rightly ruled out for offside.
Pity the travelling supporter who’d run on the pitch to celebrate his side’s first win at Stamford Bridge for six years only to find he had made his move too soon. It rather typified a match in which, for all the good intentions of both sides, moments to shout about were in short supply.
A horrendous sliding tackle on Kolasinac earned Luiz a straight red card but the 10 men of Chelsea were able to repel their hosts without undue pressure.
Chelsea starting XI: Courtois, Azpilicueta, Cahill, Luiz, Moses, Kante, Fabregas, Alonso, Willian, Pedro, Morata.
Substitutes: Caballero, Rudiger, Hazard, Bakayoko, Zappacosta, Batshuayi, Christensen.
Arsenal starting XI: Cech, Koscielny, Mustafi, Monreal, Bellerin, Ramsey, Xhaka, Kolasinac, Welbeck, Iwobi, Lacazette.
Substitutes: Mertesacker, Sanchez, Giroud, Ospina, Walcott, Maitland-Niles, Elneny.