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As befits a true legend of the game, the 38-year-old immediately shared out the glory with the teammates, family and others who have played a role in his extraordinary career.
"I love playing at this club and so this is a record for all of Juventus, not just me," Buffon told media after the game.
"It also goes to my team-mates, who do a great job in defence all over the pitch, right up to the strikers who are pressing up high, before the other team even gets near the goal."
Asked who he would dedicate the record to, Buffon said: "No one really, but I always thank my family, my partner and all the people who have been there for me through the years."
Buffon had already gone past Italian goalkeeping great Dino Zoff's Juventus record of 903 minutes without conceding, and on Sunday he needed only four minutes to make Sebastiano Rossi's Serie A record of 929 minutes, set in 1994, his own.
He passed that before seeing his run end on 973 when he failed to stop Andrea Belotti's 48th-minute penalty for Torino.
Yet on Sunday morning, the Juventus shot-stopper almost fell victim to the most human of ailments.
"This morning I was feverish and wasn't feeling good, but I couldn't even think about losing a game like this," added Buffon.
After Belotti's goal, Torino were unlucky with refereeing decisions that saw Maxi Lopez's goal wrongly chalked off for offside.
Juventus cruised to a 4-1 win when Alvaro Morata hit a brace in 14 second-half minutes to help ease the pain of their Champions League exit at the hands of Bayern Munich in midweek.
"It was important for us to bounce back with a win," said Juve coach Massimiliano Allegri.
Juve's midweek reverse in Europe follows their defeat to Barcelona in last year's final to Barcelona, and means Buffon has still never won Europe's premier club competition.
A two-time runner-up in the Champions League, in 2003 and 2015, Buffon's biggest European title at club level is the UEFA Cup he won with Parma in 1999.
A record 10-time winner of Serie A's top goalkeeper award, Buffon's record-equalling World Cup feat of five clean sheets in the 2006 edition helped steer Italy to the title, and he was pivotal as the Azzurri reached the Euro 2012 final only to be outclassed 4-1 by Spain.
Although Buffon, on 572, is still far behind fellow club legend Alessandro Del Piero (705) for the most Juventus appearances, on Sunday the 'living legend' -- as Buffon is regularly described in Italy -- made Rossi's record his own.
In an interview with Sky Sport, the 2006 World Cup-winner said: "In my career I've never thought of myself as a man of individual records.
"But this is nice, because the more you think about others, life rewards you as a person."