Italy were denied the lead when Luca Toni was wrongly ruled offside before Mutu lifted in a shot after a poor backheader to put Romania ahead.
The lead lasted barely a minute with Christian Panucci touching in Giorgio Chiellini's header across goal.
Buffon's heroics then saved Italy ahead of a final group game against France.
The tall stopper dived to his left to get a hand to Mutu's spot-kick which was then cleared after coming off his boot.
"I think Italy played better than Romania," said Azzurri boss Roberto Donadoni.
Luca Toni had a goal wrongly ruled out and Donadoni added: "I don't usually speak about referees. But the refereeing was not of high quality.
"It's funny that they saw Panucci when he was off the field against Holland and then they didn't see the player by the post.
"The error really cost us."
