Manchester City were denied a win when Gabriel Jesus saw a stoppage-time winner disallowed on review for a handball by Aymeric Laporte.
Tottenham will now travel to third-tier strugglers Rochdale for a FA Cup last-16 tie on the weekend of February 17-18.
Lionel Messi scored his fourth goal of the Copa America Centenario in the 60th minute at the Gillette Stadium to equal Gabriel Batistuta's long-time Argentina international goalscoring record
Tottenham forward Erik Lamela failed to clear in the 74th minute and the ball ricocheted around the penalty area before falling to Alex Oxlade-Chamberlain, who lashed the ball in from close range for an Arsenal equaliser. Lamela put his face in his hands after the goal in the north London derby, whose result leaves Spurs winless in four matches.