Everton continued their positive start to the season under Marco Silva with Richarlison and Gylfi Sigurdsson delivering standout performances.
Harry Kane scored his first-ever August goal but it was substitute Mousa Dembele who shifted the game back into Spurs' favour vs. Fulham.
Neither Chelsea or Arsenal will play Champions League football this season. Saturday's result showed which side is likelier to make a swift return.
After starting superbly, Maurizio Sarri's men were pegged back. However, then their trump card came off the bench to set up victory.
Maurizio Sarri admitted that Chelsea are not yet at the level of Premier League title challengers despite beating Arsenal 3-2 at Stamford Bridge.
Arsenal have lost their first two league games of the season for the first time since 1992, but Emery insisted there is no reason to panic.
Arsenal midfielder Alex Iwobi backed his new coach Unai Emery on Saturday after the Gunners suffered their second consecutive defeat.
Tottenham Hotspur manager Mauricio Pochettino believes all the players who were in his squad against Fulham are committed to the club.
Arsene Wenger has left a mess for Unai Emery but the new Arsenal boss was not helped by Pierre-Emerick Aubameyang's awful performance at Chelsea.
Marcos Alonso gets late winner at Stamford Bridge, while England striker breaks August duck against newly-promoted London rivals at Wembley.