Later, Benjani sealed the win against his old club with a fine, low strike.
City opened a 2-0 lead thanks to a brilliant curler from Stephen Ireland and Benjani's side-foot finish.
Benjani had the clearest opening of the match when his intelligent run was picked out by Kanu.
Eriksson was particularly pleased with Benjani Mwaruwari, who scored on his City debut following a move from Portsmouth.
United became stifled by a staunch City side who extended their lead with a glanced Benjani Mwaruwari header.
Defoe, 25, joined from Spurs for an undisclosed fee despite the collapse of Benjani's move to Manchester City.
However, City ran out of time to complete a move for Portsmouth striker Benjani as the transfer window closed.
When Benjani slid his shot home on 21 minutes, the writing appeared to be on the wall for the visitors.
Felipe Caicedo, Valeri Bojinov, Benjani Mwaruwari and Ched Evans have also been given shirt numbers ahead of the new season.
Benjani put in a dangerous cross early on, while Kranjcar went close with a shot from just outside the box.
Benjani waited on the ball before releasing Muntari whose angled shot to the near post trickled in underneath keeper Kingson's body.
Robinho, Roque Santa Cruz and Benjani Mwaruwari are all injured and Carlos Tevez is rated extremely doubtful to face his old club.
Almost inevitably, Benjani, who had not started since 6 November and scored once in his previous 12 appearances, made it 3-0 on 56 minutes.
City's capture of Benjani was believed to be subject to Pompey landing Tottenham striker Jermain Defoe - a deal which was completed just before midnight.
Robinho, Roque Santa Cruz and Benjani have already been consigned to the injured list and Carlos Tevez is rated extremely doubtful to face his old club.
Only a superb double stop from Gordon prevented Petrov, and then Benjani, from extending City's lead but he could not save his side from an unlikely defeat.
Left-winger Petrov was a constant threat to United with his pace and delivery and he crossed from the right for Benjani to glance in a header across goal.
Every one of the Birmingham's starting XI were up for the battle from the first whistle, although they were given an early scare when Benjani's shot struck the post.
But he was not the only guilty one as first Diop skewed his shot wide from six yards after a Benjani cross and then Taylor shot straight at Friedel.
The on-off transfer saga had been in doubt after City tried to pull out of the deal, expressing concern about a knee injury Benjani had surgery on 18 months ago.
Benjani soon wasted a glorious opportunity to extend City's lead, spinning away from his marker with a sublime first touch before blazing over with his second from six yards out.
With Jo, Benjani Mwaruwari and Valeri Bojinov also all missing, City could be forced to field teenagers Daniel Sturridge and Ched Evans in Saturday's Premier League opener against Aston Villa.
So it came as no surprise when Muntari found himself in enough space down the left to provide a wonderful near-post cross which Benjani turned in with a side-foot volley.
The penalty was given after Queudrue brought down Benjani in the area and was subsequently sent off although the decision was protested because Radhi Jaidi was also close to the action.
Eritrea looked bereft of ideas, while Zimbabwe relied on early balls to their star strike force of Peter Ndlovu and Benjani Mwaruwari, though both failed to convert after runs on goal.
Kingson, starting ahead of Maik Taylor, went some way to redeeming himself when he did well to quickly come out and put Benjani off after a free-kick cannoned into the Pompey striker's path.
"We did not pay an agent when Benjani joined from Auxerre, and his transfer to Manchester City was approved at the time by the Premier League and the FA's compliance unit, " it said.
Despite their numerical disadvantage, Portsmouth rallied and continued to conjure opportunities - although City fashioned counter-attacks through Vassell and Benjani, the latter firing wide of James's right post from the edge of the box.
Substitute Benjani Mwaruwari forced another fine save with seconds remaining, before LuaLua almost capped a fine performance with the winner with the last kick of the game - only for Niemi to save well once again.
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