Adebayor, who survived the gun attack on Togo's team bus that killed two members of their delegation before the start of this month's tournament, looked offside before he lashed the ball past keeper David James after 39 minutes.
Vincent Kompany headed the second in stoppage time at the end of the first half to put City 2-0 ahead against cash-strapped, bottom-of-the-table Pompey who remain on 15 points, five adrift of Burnley and Hull City.
"We were a little tired after Wednesday's (League Cup) match against Manchester United," Manchester City manager Roberto Mancini told the BBC.
"In the first half we did not play well, we did not move the ball quickly and were too slow when we lost possession. The clean sheet is important but it was more important that we won today."
CITY SIXTH
The victory lifted Mancini's men to sixth above Aston Villa, keeping the race for fourth spot and the last Champions League qualifying berth as intense as the race for the title.
Tottenham Hotspur are fourth with 42 points from 24 matches followed by Liverpool (41 from 24), City (41 from 22) and Villa (40 from 23).
Chelsea lead the table with 54 points from 23 games, ahead of Manchester United and Arsenal who meet at the Emirates Stadium later on Sunday.
After an opening period when Portsmouth more than matched their hosts, the game turned City's way when Adebayor netted on his first league appearance since Dec. 16.
Kompany nodded the second from a Martin Petrov corner and Carlos Tevez hit the post for the home side late in the game.
"They (City) were not the better team," said Pompey manager Avram Grant. "The first goal was in my opinion offside while the second was from a foul after a push on Tal Ben Haim.
"Their goalkeeper was more busy than our keeper. I was impressed with the players, the performance was better."
