Chile midfielder Arturo Vidal, Juve's leading scorer with 10 goals, wrapped up the title when he converted a penalty in the 59th minute amid Palermo protests after Mirko Vucinic was pushed by Massimo Donati.
Juve's celebrations were dampened when midfielder Paul Pogba was sent off in the 84th minute following a clash with Salvatore Aronica.
Klose's extraordinary afternoon began when the 34-year-old German opened the scoring in the 22nd minute.
Hernanes scored a brilliant second with a dipping 30-metre shot, then Klose grabbed two in three minutes to complete a first-half hat-trick, before adding two more early in the second half.
Bottom club Pescara were relegated after one season in the top flight when they lost 4-1 at fellow strugglers Genoa.
Antonio Di Natale scored a brilliant brace for Udinese, who beat Sampdoria 3-1, and Gonzalo Bergessio got a hat-trick to give Catania a 3-0 win over Siena, pushing their opponents closer to Serie B.
Third-placed AC Milan edged closer to the Champions League playoff spot when a late Mario Balotelli goal gave them a 1-0 win over Torino. They moved four points clear of Fiorentina who lost 1-0 at home to AS Roma on Saturday.
Juventus, needing only a point to clinch a record 29th title and their second in coach Antonio Conte's two seasons at the club, had a lucky escape when Fabrizzio Miccoli hit the post for Palermo early in the second half.
Juventus, who won their eighth successive league game, have 83 points from 35 games, 14 clear of Napoli who were hosting Inter Milan in the evening game (1845 GMT). Milan have 65 and Fiorentina 61.
At the bottom, Palermo dropped back into the relegation zone with 32 points, swapping places with Genoa who have 35. Siena, 19th in the 20-team table, have 30 and Pescara 22.
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