Birmingham caretaker boss Eric Black's first game in charge ended in a defeat to high-flying Portsmouth.
Muntari (right) is congratulated by boss Redknapp after his goal
Black chose to give Richard Kingson his debut in goal but the decision backfired when the keeper let a Sulley Muntari shot creep in under his body.
Liam Ridgewell was set to level after a piercing run before Noe Pamarot's last-ditch tackle, which Birmingham felt should have led to a penalty.
Niko Kranjcar's stunning late free-kick compounded Birmingham's misery.
The game had taken its time to get warmed up in the bitter cold at St Andrews but the home side were showing more industry at the start of the match.
They pressured the visitors and did not let them get into their normal rhythm of attacking football.
But Pompey still managed to create the first chance with Kranjcar, fresh from helping Croatia beat England in midweek, forcing Kingson to palm his shot round the post.
Birmingham responded with Mikael Forssell chesting down a ball, swivelling and shooting only for his low shot to be saved a full stretch by keeper David James.
Pompey rarely looked like a side in sixth position in the Premier League but were gifted the lead.
Benjani waited on the ball before releasing Muntari whose angled shot to the near post trickled in underneath keeper Kingson's body.
Birmingham immediately produced a spell of pressure to no avail, while Pompey grew in confidence and authority.
Portsmouth wasted a chance to extend their lead shortly after the break when John Utaka wriggled into space but, when he was about to shoot, team-mate Pamarot ran into his path and shot high.
The home crowd ramped up the noise level to try to spur Blues on but it seemed to have little effect as their efforts were not reciprocated by the team.
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.
Birmingham finally matched the passion of their supporters and rallied in the final 15 minutes.
And they had a great chance to equalise when Ridgewell was through on goal after an angled run from the left flank.
But the central defender wanted too much time to get his shot away and allowed Pamarot to slide in and tackle.
The home side felt the challenge merited a penalty but the Pompey defender appeared to have got the ball first.
Kranjcar then secured Pompey's win when he powered in a 25-yard free-kick from the right side of Birmingham's area.
Birmingham caretaker manager Eric Black:
"You've got to make decisions and play your best players. Maik has been away on international duty, Richard has been looking good and deserved his opportunity.
"It was a poor goal and no-one is more disappointed than him. At 0-0, it was not a bad result for us against a top side."
He added: "Credit to the players they gave everything they had. We'll take a lot of positives from it but unfortunately no points."
Portsmouth boss Harry Redknapp:
"We were difficult to break down and the play of our central defenders were excellent. "We have what I think is the best goalkeeper in the country in David James and with our defence that makes us difficult to break down.
"The only thing that was frustrating was that we could have really dominated but gave the ball away carelessly at times and invited pressure."
Birmingham: Kingson, Kelly, Djourou, Ridgewell, Schmitz, De Ridder, Muamba, Nafti, McSheffrey (O'Connor 74), Kapo, Forssell.
Subs Not Used: Taylor, Larsson, Queudrue, Parnaby.
Booked: McSheffrey, Kapo, Nafti.
Portsmouth: James, Johnson, Campbell, Distin, Pamarot, Utaka (Taylor 81), Diop, Davis, Muntari, Kranjcar, Mwaruwari.
Subs Not Used: Ashdown, Hreidarsson, Nugent, Pedro Mendes.
Booked: Davis, Mwaruwari.
Goals: Muntari 34, Kranjcar 82.
Ref: Martin Atkinson (W Yorkshire).