Nasri scores two as Spurs suffer KO
Teenager Henri Lansbury - one of eight changes by manager Arsene Wenger, who was serving a one-match touchline ban - swept the visitors ahead from close range on 15 minutes.
Robbie Keane, who came on at half-time, levelled three minutes after the restart, but neither side could find a winner in normal time before Nasri's spot-kick double and Andrey Arshavin's goal send the Gunners through.
Kevin Doyle spared Wolves' blushes with an extra-time double as they recorded a 4-2 victory over 10-man Notts County in their third round encounter at Molineux.
Former West Brom striker Lee Hughes looked to have had the last laugh on the Wolves boo boys by breaking the deadlock. Nenad Milijas equalised from the spot after County defender Liam Chilvers was sent off for bringing down Christophe Berra.
Substitutes Steven Fletcher and Doyle settled the tie in the first period of extra-time. Kevin Smith scored a late consolation before Doyle struck again in the last minute.
First-half goals from Michael Morrison and Lloyd Dyer saw Leicester advance to the fourth round at the expense of 10-man Portsmouth, who suffered a 2-1 loss.
A late Liam Lawrence goal set up a tense finale at Fratton Park following Richard Hughes' straight red card but Leicester held on.
Related Arsenal News