Buffon saves seal third place for Italy
Italy, who had Riccardo Montolivo sent off 10 minutes from the end of extra time for a second bookable offence, twice led only for Edinson Cavani to pull Uruguay level each time.
Cavani missed two chances to complete a hat-trick and win the match for the Copa America champions deep into extra time.
Italy finished the match utterly exhausted after playing extra time in tropical conditions for the second time in four days, following their semi-final defeat by Spain on penalties in Fortaleza on Thursday.
To make matters worse, Sunday's match kicked off at 1300 local time with most of the pitch bathed in sun. It was so hot that most of the seats in the sun were left empty with fans only taking their places after they had moved into the shade.
"It wasn't easy to give all they had when they were running on empty," Italy coach Cesare Prandelli said in a touch-line interview.
Several matches at next year's World Cup will also be played at 1300 in tropical venues, although governing body FIFA has rejected criticism and said that conditions are suitable for football.
Buffon, who saved penalties from Diego Forlan, Martin Caceres and Walter Gargano, added: "We have shown great character because today it's been really tough."
Ironically, Italy and Uruguay may have inadvertently lent weight to FIFA's argument by serving up an attractive, attacking game.
Italy took the lead in the 24th minute when Alessandro Diamanti's venomous free kick sailed over goalkeeper Fernando Muslera, hit the post and then rebounded off Muslera's back to Davide Astori, who tapped it over the line.
Uruguay got a deserved equaliser after 58 minutes when Gargano picked up the ball on the halfway line and laid it off to Cavani whose perfect side-footed finish evaded the diving Buffon.
Despite struggling, Italy went back in front against the run of play in the 73rd minute with a beautifully struck Diamanti free-kick from 25 metres.
Not to be outdone, Cavani replied with another free-kick five minutes later which Buffon flapped at and missed.
The Napoli forward could have won the match for Uruguay when he fired wide late in extra time, then slashed his shot across the face of goal after Buffon had parried Gargano's long-range shot.
"It was a great tournament but unfortunately, against Brazil and today, we didn't quite have enough," Uruguayan captain Diego Lugano, whose side were beaten 2-1 by the hosts in the semi-finals, said in a touch-line interview.