Leonardo Bonucci headed in a second-half equaliser to give Juve their first Serie A draw of the season which left them with 67 points from 27 games.
Second-placed AS Roma have 59 after Saturday's 2-1 home defeat to third-placed Napoli, who are a further two behind.
Palermo, who remained seven points adrift of safety in the relegation zone, went ahead on the half hour when Andrea Rispoli charged forward and beat Joe Hart from 20 metres.
The Sicilians, playing their first match since flamboyant president Maurizio Zamparini resigned last week, stayed in front until Belotti sprang into action late in the game.
The 23-year-old Italy forward, who spent two seasons at Palermo, headed the equaliser in the 74th minute, then struck again two minutes later when he met Adem Ljajic's free kick with a superb volley.
Serie A's leading scorer completed his hat-trick and took his season's tally to 22 with another header in the 81st minute after Palermo goalkeeper Josip Posavec again failed to deal with a cross.
Udinese stunned Juventus eight minutes before halftime when Duvan Zapata burst down the left, held off a challenge from Bonucci and scored with an angled shot that squirmed under Gianluigi Buffon.
Bonucci levelled on the hour and Juve appeared happy with that, even though the result ended a run of 10 successive wins in all competitions.
Ivan Perisic scored twice to lead Inter Milan to a 5-1 win at Cagliari while Genoa won 2-0 at Empoli with late goals from Olivier Ntcham and Oscar Hiljemark. Crotone's match at home to Sassuolo ended in a goalless stalemate as did Atalanta's meeting with Fiorentina.
(Writing by Brian Homewood in Berne; Editing by Clare Fallon)
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