Jermain Defoe's 100th goal for Tottenham looked to have given the home side the win after Roman Pavlyuchenko had equalised Peter Odemwingie's fifth-minute opener.
But with nine minutes remaining, Cox dipped a wonderful 20-yard shot over Heurelho Gomes' head to steal a point and leave Spurs one point behind fourth-place City, who play their match in hand against Blackburn on Monday.
The result was a bitter blow for Redknapp and his men, who had their tails up after Wednesday night's thrilling comeback against Arsenal.
Spurs will now hope relegation-threatened Rovers will surprise Roberto Mancini's men and it may be that the Londoners have to win all five of their remaining matches - which include tough fixtures against City, Chelsea and Liverpool - to make it into the Champions League for the second year running.
Source: PA
Source: PA