Midfielder Jose Mauri, 18, scored on the hour as Juventus, 7-0 winners over Parma earlier in the season, suffered only their second league defeat of the campaign.
Even though the leaders rested several players ahead of their Champions League tie with Monaco on Tuesday, it was still a remarkable result for Parma who have only continued in the league thanks to a fund set up by the Italian federation.
Juventus remained 14 points clear at the top and on course for a fourth successive title while Parma, who have had three points deducted for breaching financial regulations, are on 16 points, still five adrift at the bottom.
Parma, who at one stage had to postpone two successive games due to their financial problems, have taken seven points from their last three outings, but remain 10 points from the safety zone with nine matches left.
Genoa beat one-from-bottom Cagliari 2-0, pushing the Sardinians (21 points) closer to Serie B, and Inter Milan won 3-0 at Verona to end a seven-match winless run in all competitions.
Roberto Mancini's side are joint eighth alongside AC Milan and Genoa with 41 points.
"This has given us great satisfaction in a very difficult season," said Parma coach Roberto Donadoni.
"Everyone is making a great sacrifice. I must pay my compliments to the lads who are doing something extraordinary."
"To be captain today against Juve and win in this situation is something I will never forget," added captain Massimo Gobbi. "This is the sort of story that can only happen in sport."
Juventus coach Massimiliano Allegri criticised his team.
"Today was an important match, but we didn't understand that," he said on the club's Twitter feed. "We didn't control the match and we deserved the defeat."
"The absent players are no excuse," he added later in the press conference. "We didn't win a tackle out there and that tells you a great deal about the spirit Parma played with."
Juventus rested strikers Alvaro Morata and Carlos Tevez along with playmaker Andrea Pirlo, who had recovered from a calf injury, while goalkeeper Gianluigi Buffon had a stomach virus.
Parma goalkeeper Antonio Mirante kept the hosts in the game in the first half but Parma broke through just after the hour when Ishak Belfodil, always a threat on the break, burst down the right and pulled the ball into the middle for Mauri to sidefoot into the top corner from just inside the area.
There were some bad-tempered exchanges as Juventus pressed for an equaliser, but Parma held out to give Donadoni his first Serie A win over Juve in 10 attempts as a coach.
Mauro Icardi gave Inter an 11th minute lead at Verona, tapping in Rodrigo Palacio's low cross for his 16th Serie A goal of the season as the home defence appeared to be distracted by an apparent injury to Panagiotis Tachtsidis, who quickly recovered.
Palacio extended Inter's lead after halftime before their goalkeeper Samir Handanovic continued his remarkable run of penalty saves by denying Luca Toni from the spot.
The Slovenian has saved seven of the last eight penalties against him.
An unlucky own goal by Vangelis Moras in stoppage time completed Inter's win.
(Writing by Brian Homewood, editing by Pritha Sarkar)
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