The draw pushed Chelsea up a place into fourth spot in the Premier League, level on points with third-placed Spurs and one point ahead of Arsenal, both of whom have a played a game less.
Arsenal's best chance to equalise came from a Granit Xhaka free kick which looked destined for the top corner until the Gunner's former keeper Emiliano Martinez at full stretch pushed it around the post with a fingertip save.
Liverpool a dramatic 2-1 victory over Leicester City at Anfield, thus maintaining the league leaders' 100 per cent start
Burnley struck either side of halftime with headers from Jeff Hendrick and Michael Keane to claim a 2-0 Premier League home win over Watford on Monday in the first top-flight meeting of the two clubs.
Former England hero Paul Gascoigne has said the current team under Roy Hodgson lack the passion he was famous for, and that he cannot bear to watch much football these days because he misses playing so much.
News of all that's transpired on and off the football field
England created numerous chances but Calvert-Lewin's penalty was the only addition to the score as the hosts impressed ahead of Nations League clashes against Belgium and Iceland.
Two goals each for Roberto Firmino and Sadio Mane helped Liverpool to keep in touch with Premier League leaders Manchester City with a 4-2 win over lowly Burnley at Anfield on Sunday.
Lacazette fired the Gunners ahead in the eighth minute after poor defending by the home side before new signing Gabriel made it 2-0 in the 49th and Aubameyang put the icing on the cake with a superb shot into the top corner.
A Ciaran Clark own goal earned Sweden a fortunate 1-1 draw against a spirited Ireland side in their Euro 2016 Group E opener at the Stade de France on Monday.
But for third-placed Spurs, who trail leaders Manchester City and Liverpool by five points, this may prove to be a loss that leaves them with too much ground to make up.
Images from the English Premier League matches played on Sunday
Ireland reached the knockout phase at a European Championship for the firs time when Robbie Brady's late goal earned them a 1-0 victory against Group E winners Italy on Wednesday.
Images from Sunday night's English Premier League matches.
Images from the English Premier League matches played on Saturday.
Liverpool had won each of their previous four home leagues games in which they conceded first and 12 minutes later they had turned another match on its head as Roberto Firmino's trickery set up Mane to give the hosts the lead at the second attempt.
IMAGES from Saturday's English Premier League matches.
IMAGES from the Euro 2020 qualifiers
Spain started their World Cup qualifying campaign with a crushing 8-0 win over Liechtenstein, laying down a marker in Group G with a ruthless second-half display on Monday.
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