Eddie Howe's side led 3-0 midway through the second half thanks to goals from Charlie Daniels, Callum Wilson and Ryan Fraser.
But the Gunners salvaged a dramatic point through Alexis Sanchez, Lucas Perez and a 91st minute header by Olivier Giroud.
Simon Francis was also shown a straight red card for the home side.
Elsewhere Swansea City put their poor form behind them with a crucial 2-1 win away to Crystal Palace – Angel Rangel getting the late winner for the visitors.
And Stoke were 2-0 winners at home to strugglers Watford.
Meanwhile
Tottenham will be hoping to put an end to Chelsea's incredible run of wins when they meet in a crucial Premier League tie this evening.
A win for Chelsea would see them equal Arsenal's record of 14 straight wins in a single season.
Three points for Spurs meanwhile would see them once again leapfrog Manchester City into the top 4 on goal difference.
Chelsea boss Antonio Conte has acknowledged his side have become the team to beat.
