Boateng, who played for the Black Stars at the 2010 World Cup, swept home the first goal just before the hour and Muntari, back after missing the first half of the season with a knee injury, blasted a superb second.
"It was definitely the most important goal of my career," Muntari, famous for his blistering left-foot shot, told reporters.
"We knew it would not be easy but that we could do it," he said. "We were disciplined, blocking out Barcelona's game."
The two players, however, have very different relationships with Ghana.
Muntari, who has more than 10 years experience of European football, has won 75 caps for the Black Stars and has played regularly for the side since 2003.
Boateng was raised in Germany, playing for them at youth level, but chose to play for Ghana at the 2010 World Cup after being approached by the country's football association.
However, the following year he angered Ghanaians by announcing his international spotlight, prompting suggestions that he won his transfer to Milan on the back of his excellent performances at the 2010 World Cup, when Ghana reached the quarter-finals.
Milan coach Massimiliano Allegri paid another tribute to club president Silvio Berlusconi after the famous win.
"We dedicate this to the president, because he has given me a team I can work with," said Allegri, who before the game said he frequently discusses tactics with the former Italy Prime Minister.
"This is a team I can help improve and we have to forget a bit about what happened earlier in the season," added the coach.
Milan sold off several players at the end of last season to cut costs and struggled at the start of this term as Allegri was forced to rebuild.
