It was the first time since Dec. 9 that the Turin side had failed to win a league game and the result breathed new life into the Serie A title race just as Juventus had threatened to break clear.
Although Juventus moved five points ahead at the top, second-placed Napoli's fate is back in their own hands as they host Genoa on Sunday, when they can cut the lead to two points, and still have to meet Juve in mid-April.
Juventus, who completed their 10th league game without conceding a goal, dominated possession but were unable to find a way past SPAL's resolute defence.
SPAL's Filippo Costa did well to block Alex Sandro after he was sent through by Douglas Costa and Paulo Dybala curled a Juventus free kick on to the roof of the net just before halftime.
Mario Mandzukic had Juve's best second-half chance when he met Costa's cross with a diving header but his effort went wide.
SPAL, who are back in Serie A after a 49-year absence, moved one point and one place clear of the relegation zone. A capacity 13,000 crowd at their modest stadium celebrated the final whistle as if they had won a title.
"I'm not angry or disappointed, we were up against a SPAL side who fought hard and believed in themselves," Juventus coach Massimiliano Allegri said.
"They were very aggressive and they committed a lot of fouls, but these aren't excuses."
Allegri warned that Juve would face similar tough matches against other relegation candidates.
"This match should be a lesson for when we play Benevento and Crotone, who are fighting for survival and will make things difficult," he said.
SPAL captain Mirco Antenucci said the result was "something to be proud of, it's very satisfying".
Sassuolo ended a nine-match winless run by beating Udinese 2-1 in Saturday's other game and handed their opponents a fifth successive loss.
Sassuolo went ahead thanks to an own goal when Stefano Sensi's corner ricocheted off Ali Adnan and into the net in the 42nd minute
Seko Fofana equalised two minutes later by curling an exquisite effort into the top corner, a goal which was confirmed after a review by the video assistant referee (VAR).
Sensi turned in Matteo Politano's cross for the winner in the 74th minute.
(Writing by Brian Homewood in Bern,; Editing by Ed Osmond)
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