Leroy Sane scored inside five minutes as fourth-placed City started brightly in their bid to put breathing space between themselves and those on their coat-tails in the hunt for a Champions League spot.
Walcott responded after a clumsy mistake from Gael Clichy, and Shkodran Mustafi grabbed a point for the Gunners with a second-half header after Sergio Aguero's drilled effort before the break.
The Gunners have won just once in their last six Premier League matches and remain seven points outside the Champions League places.
EPL | The Premier League table after 30 matches
Tottenham cut Chelsea's lead at the top of the Premier League table to just seven points with a hard fought 2-0 victory over Burnley on Saturday.
Mauricio Pochettino lost Victor Wanyama and Harry Winks to injury but saw his side produce a stirring second-half performance in order to secure a crucial win at the expense of Sean Dyche's side.
Eric Dier and Heung-min Son were the men on target at Turf Moor as the north Londoners proved, yet again, that they can cope without talisman Harry Kane.
Pacesetters Chelsea did not fare so well and suffered a damaging 2-1 defeat to capital rivals Crystal Palace.
Cesc Fabregas struck early to suggest the Blues were on course for a straightforward victory but Wilfried Zaha and Christian Benteke hit back to blow the title race wide open.
The Eagles' performance may have affected the battle at the top but Sam Allardyce will be more concerned with events at the bottom.
Palace are now four points clear of the drop zone and two points behind West Ham, who lost at relegation threatened Hull City.
Meanwhile, Manchester United endured another goalless draw on home turf as Tony Pulis' West Brom frustrated Jose Mourinho.
Liverpool are third, having beaten Everton in Saturday's early kick-off, while Arsenal and Manchester City are not in action until Sunday afternoon.