The Turin side had wrapped up their 29th Scudetto title last weekend with a narrow victory over Palermo and their next target was beating their own points record set in 2006 under Fabio Capello.
However, today proved to be a damp squib as they were shocked by the visitors who took the lead through Victor Ibarbo after 12 minutes before Vucinic levelled after 61 minutes.
Juve were the first to show with Cagliari goalkeeper Michael Agazzi forced to save Arturo Vidal's 30-yard shot which was heading for the corner.
Cagliari were ahead a minute later with a fine solo goal from Ibarbo who passed Claudio Marchisio and Andrea Barzagli before moving inside the box and scoring in the bottom left-hand corner.
Emanuele Giaccherini shot high and wide for the hosts before Radja Nainggolan sent an effort narrowly wide of the right post as the visitors took the game to the champions.
Agazzi saved well in the bottom right-hand corner from Marchisio before Juve almost levelled when the goalkeeper was well beaten by Sebastian Giovinco's free-kick which smashed against the bar.
Juve had built up a head of steam with Alessandro Matri twice shooting over as they failed to pierce the visiting defence before half-time.
Ibarbo shot over for Cagliari but Juve started the second half as they finished the first but they found Agazzi in inspired form.
An unmarked Giaccherini was denied by the keeper at his near post and he then blocked Matri's turn and shot before Vucinic fired over.
However, Cagliari's resistance was ended with a little under half an hour remaining.
Marchisio crossed from the left was headed on by Vidal with Agazzi failing to take the catch and Vucinic tapping in.
Marchisio then skimmed the post with a header and Mauricio Isla's drilled shot went narrowly over as Juve searched for the winner.
Cagliari showed they were not a spent force when Nainggolan's right-footed shot from outside the box was only narrowly wide as the game finished in a draw.