Miko Vucinic put the Bianconeri in front in the sixth minute and an own goal from Michele Canini in the second half earned Antonio Conte's side the win, sparking scenes of joy on the pitch at the Stadio Nereo Rocco.
Juve will now pick up the trophy at their final game of the season at the Juventus Stadium against Atalanta next weekend.
Vucinic broke from a borderline offside position to reach Leonardo Bonucci's ball forward and he kept his cool to slot the ball through the legs of Michael Agazzi to put Juve in front on their first attack in the sixth minute.
Andrea Pirlo tried his luck from 25 yards, but Agazzi denied him, as he did moments later as Simone Pepe had Juve's next effort in a buoyant opening from the visitors.
Mauricio Pinilla came close to equalising for Cagliari with a speculative shot from 35 yards which went just inches wide of the post, but Pepe then flashed a shot across Agazzi's goal as Juve continued to look for a second goal.
Cagliari tried to make a fight of it early in the second half, and with the news filtering through that Milan had taken the lead against Inter, Juve started to look a little nervous.
But substitute Marco Borriello settled their nerves as he did enough to disturb Canini, who put Martin Caceres' cross into his own goal in the 74th minute, leaving his own goalkeeper no chance.
Juve just played down the clock as the fans started to celebrate, and with the news arriving that Inter had turned the game around against Milan and were 4-2 ahead, even Conte and the Juve bench started to celebrate the inevitable.
The final whistle was met by a pitch invasion as the estimated 15,000 Juve fans who had made the trip to Trieste started celebrating the Scudetto with one game of the season to go.