Pierre-Emerick Aubameyang's strike ruined Newcastle manager Steve Bruce's first match in charge of the club he supported as a boy.
Luis Suarez scored the winner in the 89th minute in front of nearly 99,000 people, who packed the stands to see new signings Antoine Griezmann and Frenkie De Jong.
Unai Emery insisted his side's Europa League semi-final against Valencia is still "50-50" despite Arsenal taking a 3-1 first leg lead to Spain.
Arsenal held out for a first clean sheet away from home in the Premier League this season to move ahead of Chelsea on goal difference into fourth.
Apart from Pierre-Emerick Aubameyang, substitute Alex Iwobi scored the third goal for Arsenal while Ashley Barnes scored the lone goal for Burnley.
A video has emerged that appears to show a number of Arsenal stars inhaling nitrous oxide.
A banana skin was hurled from the away end at the Emirates Stadium as Pierre-Emerick Aubameyang celebrated scoring in front of the Tottenham fans.
Aubameyang's superb long-range equaliser sparked a second-half surge from Arsenal.
Arsenal have been revitalised since Unai Emery replaced Arsene Wenger in the close-season.
Arsenal take on Sporting CP while Chelsea take on Bate Borisov in their Europa League encounters.
Arsenal's third goal was one of the best team goals scored in the Premier League this season.
Arsenal swept to their 10th successive win with a dominant 3-1 victory against Leicester.
Arsenal turned on the style against Fulham, recording their biggest win of the season.
Arsenal defeated Ukraine's Vorskla Poltava 4-2 in the Europa League, while in-form Chelsea registered a 1-0 win away to PAOK in Greece.
Christan Eriksen's wonder strike levelled in first-half stoppage time, before Alli took centre stage to end a barren run by his standards with two smart finishes just after the hour mark.
This was Arsenal's eighth defeat this year and their fourth straight league defeat.
Pierre-Emerick Aubameyang's lively debut was aided by three assists from Henrikh Mkhitaryan in his first Arsenal start.