Ireland lit up an otherwise poor match when he made a cracking connection with Darius Vassell's cross from the left.
Darius Vassell gave City the lead from the spot early in extra time after the first 90 minutes finished goalless.
BBC: SPORT | Football | League Cup | Doncaster 1-1 Man City (aet)
Darius Vassell's pass across the box finding the midfielder after Michael Johnson had intelligently let the ball run through his legs.
Our hero was soon limping, it became clear he could not carry on and he was eventually replaced by Darius Vassell.
It was a great feeling when Darius Vassell scored our first goal and, when the second went in, it was almost unreal.
Vassiriki Diaby dispossessed Darius Vassell with a crunching tackle and fed Eboue, whose whipped cross from the right was clinically despatched by Rosicky.
Hughes' plans for the new season suffered a blow on Tuesday when Darius Vassell was ruled out for 10 weeks with a knee injury.
Pompey were a man down just before half-time when Hermann Hreidarsson was sent off for impeding Darius Vassell as the City forward ran through on goal.
Darius Vassell put City in front after a defensive mix-up on 10 minutes, with Martin Petrov doubling the lead with a deflected strike two minutes later.
Hughes has released former England international striker Darius Vassell, while England Under-20 forward Daniel Sturridge has joined Chelsea for a fee to be resolved by a tribunal.
Gregory is likely to name an unchanged side with Ugo Ehiogu and Darius Vassell injured and recent signing Benito Carbone cup-tied after playing in the competition for Sheffield Wednesday.
Darius Vassell came off the bench to provide a brief moment of hope when he was played in by teenager Michael Johnson on his City debut, but the striker shot wide.
Striker Darius Vassell also pulled out on Tuesday with a stomach upset but there was better news for Eriksson as skipper David Beckham has shaken off a slight knock and will definitely play.
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