Cole's dismissal had come shortly after a Glen Johnson shot had been tipped over the bar by Arsenal keeper Manuel Almunia and an Ngog header from a Gerrard corner had been cleared off the line by Gael Clichy.
The first came following a kick by Briers which rebounded off the bar straight into the hands of Johnson, before he added one of his own when he intercepted Simon Finnigan's pass.
His opposite number Sergey Narubin was the busier and the Perm keeper pushed a decent shot from Johnson away before Dempsey's follow-up was cleared over the bar.
Defoe had netted five goals in his last five Premier League matches but could not add to that run when he cracked a right-foot shot high over the bar after cleverly peeling off a posse of defenders to meet Johnson's smart free-kick.