Italy knew a defeat would send them crashing out and, after seeing Romania stifle and squeeze France to a goalless draw, they drafted in the creative Alessandro del Piero to help unlock their stubborn opponents.
Del Piero came close to justifying his selection when his header was deflected wide at the near post as Italy exerted some early pressure.
But the resilient Romanians fended off their rivals and responded by going close three times as they showed signs of releasing the shackles from their play against the French.
Mutu was put through one-on-one with Buffon and saw his angled drive well-saved.
Buffon was quickly back in action to palm away a sweetly-struck 30-yard shot from Gabriel Tamas before Italy breathed a collective sigh of relief when defender Panucci flicked a Christian Chivu free-kick against the post.
Romania had to replace Mirel Radoi after a clash of heads with Razvan Rat as the Azzurri regained the initiative but were denied the lead through a mixture of poor finishing and desperate Romanian defending.
Mutu reflects on his penalty miss against Italy
Toni and Del Piero were each off target with headers before a last-ditch Paul Codrea lunge diverted a Simone Perrotta close-range effort wide.
Romania keeper Bogdan Lobont dived at full length to keep out two Toni headers in quick succession during a flurry of goalmouth action.
Toni finally nodded the ball home from Gianluca Zambrotta's cross just before the interval only to be marginally ruled offside as fans caught their breath after an exciting first half.
The match continued in the same vein after the break and an explosive minute of action saw both teams score.
Mutu pounced on Zambrotta's poor backheader to put Romania ahead only for Panucci to level when he touched in Chiellini's header.
There was little sign of a let up in the game as Italy pressed for a winner with the inspired Lobont saving a Daniel De Rossi header to keep his side level.
The late drama came when the referee awarded Romania a penalty when Panucci dragged down Daniel Niculae only for Buffon to rescue his side.
Italy now play France on 17 June, while Romania simultaneously face the Netherlands.
Italy: Buffon, Zambrotta, Panucci, Chiellini, Grosso, Camoranesi (Ambrosini 85), Pirlo, De Rossi, Del Piero (Quagliarella 77), Perrotta (Cassano 58), Toni. Subs Not Used: Amelia, De Sanctis, Gamberini, Barzagli, Gattuso, Di Natale, Borriello, Aquilani, Materazzi.
Booked: Pirlo, De Rossi.
Goals: Panucci 56.
Romania: Lobont, Contra, Tamas, Goian, Rat, Radoi (Dica 25), Petre (Nicolita 59), Codrea, Chivu, Mutu (Cocis 88), Daniel Niculae. Subs Not Used: Popa, Stancioiu, Marica, Sapunaru, Ghionea, Moti, Marius Niculae, Cristea, Radu.
Booked: Mutu, Chivu, Goian.
Goals: Mutu 55.
Ref: Tom Ovrebo (Norway).
BBC Sport Player Rater man of the match: Italy's Gianluigi Buffon on 7.64 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
Both countries can still qualify for the next round.
Adrian Mutu's missed penalty was the third penalty miss against Italy in four attempts in European Championship history (excluding penalty shoot-outs).
A day after Ivica Vastic became the oldest goalscorer in the history of this tournament, 35-year-old Christian Panucci became the second oldest player to score at a European Championship. Before today, Alessandro Altobelli was the oldest Italian to score in a European Championship match, when netting against Denmark (2-0) at Euro 1988 at the age of 32 years and 202 days.
Reigning world champions Italy are in danger of being knocked out in the group stage. The last two reigning world champions from Europe went on to at least reach the final of the next European Championship.
Dorin Goian is suspended for the final group match against the Netherlands. Goian scored the only goal when these teams last met in a European Championship qualifier on 13 October 2007.
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