Olivier Giroud came off the bench to earn Arsenal a 1-1 draw at Manchester United on Saturday.
Arsenal missed the chance to go top of the Premier League as they were held to a 1-1 draw by Tottenham at the Emirates on Sunday.
Manchester City, Arsenal and Liverpool remain in a logjam atop the Premier League after each won away on Saturday.
Arsenal hit top spot in the Premier League on Saturday but were still frustrated as they could only draw 0-0 with struggling Middlesbrough.
Late goals were the order of the day on Saturday as Manchester City and Chelsea maintained their winning starts to the Premier League season.
Arsenal manager Arsene Wenger said his players were "not physically ready" for the start of the season after they were beaten 4-3 at home by Liverpool on Sunday.
Manchester United made a winning start under Jose Mourinho and Liverpool won 4-3 at Arsenal in a seven-goal thriller on Sunday.
Arsenal ended a run of four league games without victory as they won 2-0 at Bournemouth on Sunday to go joint-second in the Premier League.