Juve, who have made a stuttering start to their attempt to win a fifth successive league title, went ahead five minutes into the second half when Simone Zaza scored with a shot on the turn from the edge of the penalty area.
Frosinone, whose own stadium holds only 10,000 people, appeared to be heading for their fifth straight defeat until Leonardo Blanchard headed in from a corner in stoppage time after he was left unmarked by the Juve defence.
Juve were left joint 12th alongside Atalanta with five points.
Felipe Melo's powerful header gave Inter a 1-0 win over Verona and left Roberto Mancini's Inter as the only team with 15 points from five games, all of them by one-goal margins.
The bruising Brazilian midfielder outjumped his marker to head home in the 56th minute, just after Jacopo Sala had hit the crossbar at the other end.
An embarrassing own goal by Kostas Manolas sent AS Roma crashing to their first defeat as they were went down 2-1 at Sampdoria, who are joint fourth with 10 points alongside Chievo and Torino.
The Greek defender took a wild swipe as he attempted to clear Eder's cross, mis-kicked completely and sent the ball into his own goal five minutes from time.
Eder had given Sampdoria the lead early in the second half and Mohamed Salah scored for the second game in a row to equalise for Roma.
Fiorentina went second with 12 points when second-half goals from Jakub Blaszczykowski and Nikola Kalinic gave them a 2-0 win over promoted Bologna.
Sergio Floccari gave surprise package Sassuolo a 1-0 win at Palermo to put them third (11 points) and Chievo beat Torino by the same score.
Napoli, who thumped Lazio 5-0 on Sunday, were held 0-0 at Serie A newcomers Carpi, who picked up their second point of the campaign. Lazio, meanwhile, beat Genoa 2-0.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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