But against a better class of opposition City could well have struggled, as they appeared to be suffering a hangover from their midweek Carling Cup semi-final defeat against Manchester United.
Apart from a brief spell before half-time, when City scored their two goals, it was a laboured performance in which Pompey, without a won at City since 1963, were far from second best for lengthy periods.
Indeed, it was hard to believe that virtually the whole length of the table separated the two teams such was the nature of the game in which City's victory came at a cost after they lost defenders Pablo Zabaleta and Vincent Kompany through injury.
Kolo Toure and Emmanuel Adebayor returned from the Africa Cup of Nations while there were also recalls for Martin Petrov and Stephen Ireland, as Roberto Mancini made four changes from the starting line-up for their Carling Cup semi-final as Micah Richards, Craig Bellamy, Dedryck Boyata and Shaun Wright-Phillips lost out.
Pompey made the livelier start in which John Utaka and Jamie O'Hara had decent chances, while Danny Webber might have won an early penalty after appearing to be shoved off the ball by Javier Garrido.
It was not until midway through the opening half that City began to threaten when Petrov and Kompany both saw efforts fly narrowly wide.
There was another let-off for City when Anthony Vanden Borre's shot took a deflection off Kompany and looped over keeper Shay Given before hitting the crossbar.
City's nerves were soothed when Adebayor broke the deadlock in the 40th minute running on to an Ireland through ball and shooting high into the roof of the net from the edge of the box.
And they doubled their advantage in first-half stoppage time when Kompany headed home Petrov's corner to leave Pompey with a mountain to climb.
In fairness to Pompey, they took the game to City and more than matched their more illustrious opponents in a second period of few chances, though Carlos Tevez came close to adding a third goal after his shot struck the upright.