Liverpool's Sadio Mane inspired their win at Southampton.
Mauricio Pochettino's side claimed a dramatic draw thanks to Lucas Moura's header 19 seconds after his introduction off the bench, before Gabriel Jesus had a stoppage-time victor chalked off as replays showed the ball hit Aymeric Laporte on the arm moments earlier.
After VAR helped Spurs go through in the Champions League quarterfinals against City last season, it helped them get a draw here as a handball was called on Aymeric Laporte just before Gabriel Jesus looked to have scored the victor in added time. There were a few sloppy moments and we obviously conceded two goals which could have been prevented.
Sergio Aguero restored City's lead 10 minutes before the break, with the excellent Kevin De Bruyne once again the provider with a low ball.
Roberto Firmino doubled the lead on 71 minutes before Danny Ings was gifted a goal on 83 minutes by a howler from Reds goalkeeper Adrian.
However, as the Liverpool players thronged around Adrian to congratulate him on his match-winning penalty save to thwart Tammy Abraham, a supporter ran from the stands to join in the celebrations and somehow managed to injure the goalkeeper's ankle in the melee.
Aubameyang won it, though, firing past Pope after Ceballos robbed Johann Gudmundsson in midfield - the Gabon striker now has seven goals in four league games against the Clarets.
"I'm sorry I have to score but I'm wearing a Liverpool shirt now".
Arsenal's Matteo Guendouzi in action with Burnley's Jay Rodriguez Action during their English Premier League match at Emirates Stadium in London August 17, 2019.
Arsenal manager Unai Emery gave first starts to new signings David Luiz and Dani Ceballos, with the latter involved immediately, setting up Alexandre Lacazette for Arsenal's opener.
Barnes gave Luiz a hard time as Burnley drew 2-2 away to Chelsea at the end of last season and the Brazilian can expect more physical play this time around.
Play-off winners Aston Villa's wait for a first win of the season goes on, however, as they lost 2-1 at home to Bournemouth.
Everton boss Marco Silva enjoyed a 1-0 win against his former club Watford at Goodison Park.
Liverpool began their campaign with a 4-1 win at home to newcomers Norwich as well as a victory against Chelsea in the European Supercup after penalties on Wednesday night, to lift their first title of the new season.