Everton striker Ayegbeni Yakubu gave Nigeria the lead in the 34th minute from the penalty spot, but Michael Essien headed in the equaliser off the post from Muntari's cross in the 45th.
"Today they are heroes,'' Ghana coach Claude Le Roy said.
"To come back with 10 players against a team like Nigeria and to deserve to win ... I am so proud to be the boss of this team.''
Yakubu's superb pass released Peter Odemwingie in the 60th, forcing John Mensah into a clumsy foul.
The Ghana captain was shown a straight red card by referee Mohamed Benouza.
It was the second sending off of the tournament, and meant Essien dropped back in defence as an emergency center half.
"I made the choice not to introduce new players and asked Michael to play in defense,'' Le Roy said.
"I tried to win the game. I just asked the players to stay organized. Sulley, especially, was the boss in midfield.''
The Black Stars went into halftime to loud cheers at the Ohene Djan stadium, while Nigeria's Super Eagles formed a circle for several moments to regain their composure.
Ghana's goalkeeper Richard Kingson (C) fails
to stop a penalty from Yakubu Aiyegbeni [AFP]
Nigeria took the lead when Eric Addo fouled Ikechukwu Uche and Yakubu scored for the second straight match.
Ghana had started well, with Asamoah Gyan hitting the post after a solo run in the 25th. Yakubu spurned a chance for Nigeria in the 12th and Uche poked his shot straight at goalkeeper Richard Kingson in the 32nd.
"I have to congratulate Ghana, but you can't afford to make mistakes,'' Nigeria coach Berti Vogts said.
"I am very disappointed that we lost, but you saw that the Ghana team had a lot more experience. Most of them played in the World Cup.
"We can hold our heads up, because we gave 100 percent today.''
Le Roy kept faith with 21-year-old Anthony Annan in a holding midfield role after he impressed in the last group match against Morocco.
Winger Laryea Kingston was relegated to the bench.
|Ghanaian fans celebrate in a open air market in|
Tamale, Ghana [AFP]
Ghana lost to the Nigeria at the 2006 African Cup, and Ghana beat the Super Eagles 4-1 in a friendly last year.
Everton captain Joseph Yobo had to cover for numerous mistakes from Nigeria's other defenders, and goalkeeper Austine Ejide's uncertainty on crosses and corners left the Super Eagles vulnerable.
With seconds left before halftime, Essien timed his jump well and Ejide was rooted to the spot as Ghana leveled.
Yakubu almost scored within a minute of the restart when he collected Kingson's poor clearance and lobbed the ball toward goal, forcing Kingson to track back desperately and tip over for a corner.
Odemwingie tested Kingson again in the 52nd after running onto a big clearance from Ejide. He raced through again moments later, but was thwarted by a late call for offside.
Nigeria defender Taye Taiwo was caught well out of position in the 56th, but Gyan's poor first touch meant he failed to take advantage and Le Roy replaced him with Kingston.