The Azzurri trailed 1-0 at half-time but hit back with second-half goals from Giorgio Chiellini and Mario Balotelli.
"I want to thank Chiellini and Balotelli for the goals," Buffon told the Italian media. "Now we can fully celebrate."
Buffon had cause for double celebration as he equalled the record of 136 international appearances set by former Italy captain and defender Fabio Cannavaro in Turin.
"I dedicate my record to this group considering what we have built in the past few years with (Italy coach Cesare) Prandelli," the Juventus goalkeeper added.
"I also want to thank the fans, who have supported the national team with passion and this has been crucial for us.
"But the biggest satisfaction for me is to have earned a ticket to Brazil."
Prandelli was equally delighted with the fighting spirit shown by his players at the Juventus stadium.
The four-time World Cup winners dominated possession against the Czechs but paid the price for Balotelli squandering a clutch of quality chances in the opening half.
"Balotelli's mistakes? It happens that a striker misses chances in those moments," Prandelli said. "I told him to be calm and that he was doing a good job.
"I saw a great Italy.
"We created four goalscoring chances in the opening half and I told my players to believe it was possible because we were making chances for ourselves."
The victory in Turin leaves Italy unbeaten in Group B and seven points clear of nearest rivals Bulgaria, who beat Malta 2-1 on Tuesday.
"We are a special team," Prandelli said. "In recent years we have proved that we know our limits and that we can enhance our quality.
"Now we must remember that we can still improve.
"We will think about the World Cup with calmness."
The Italians have now won six of their eight qualifying matches and clinched their place in next year's tournament in Brazil with two games to spare.