The Bees had a good start at Gtech Community Stadium, taking the lead twice before Spurs got their rhythm in the game.
Kaoru Mitoma and Tariq Lamptey were both on target in the second half as Arsenal were knocked out of the English League Cup in the third round.
Manchester United defeated Sheriff 3-0 to keep the hope of top place finish alive.
Antonio Conte’s frustration is set to increase, with the Tottenham manager expected to be banned for next week’s crucial UEFA Champions League match at Marseille.
Ronaldo was axed from the United first team squad by coach Erik ten Hag last week as reprimand for walking off the pitch before full time.
Newcastle United beat Tottenham 2-1 on Sunday to move up to fourth in the English Premier League (EPL).
Leicester City have now failed to win a Premier League game this season.
Manager Antonio Conte said he was pleased with the result, but echoed Kane in saying that his team can do more.
Tuchel and Conte were sent off after the highly tense match marred by poor officiating.
