Alberto Gilardino's first-half goal gave Italy the lead in the 2014 FIFA World Cup qualifier in Palermo, but it had captain Buffon to thank for earning a vital three points as he pulled off several top-class saves as the visitor pressed hard for the equaliser after half-time.
Italy is now all but assured of reaching Brazil next year, as the result leaves it seven points clear of Bulgaria at the summit of Group B in the European qualification section, but coach Prandelli knows his side rode its luck against its rival.
"Gigi (Buffon) saved the result with an extraordinary performance, so it's nice to suffer and still win," he told RAI Sport.
"Bulgaria poured forward towards the end, they gambled it all, so it was predictable we would suffer."
The former Fiorentina coach was forced into making several changes for the game, with Mario Balotelli, Pablo Daniel Osvaldo and Riccardo Montolivio all unavailable.
And Prandelli felt these alterations was partially responsible for his side's poor performance.
"Unfortunately tonight we had to make three changes due to injuries so it became complicated," he added.
"Our fitness levels are not optimal and that makes it all much more difficult."
Italy now needs only one win from its remaining three games to secure its place at next year's finals, and it has an opportunity to do so when it entertains Czech Republic - which succumbed to a home defeat to Armenia - in Turin on Tuesday evening (Wednesday morning AEST).
"We'll try to get as many players as possible back to fitness," Prandelli went on to say.
"The Czechs are also gambling their last chips, so I warn you it is not going to be a walk in the park, but we'll give it our all too. We're fired up."