Mauro Icardi gave the Nerazzurri a lead which would have seen them rise to fifth had they been able to see it through to the end.
However, a Claudio Marchisio penalty and Alvaro Morata strike saw Juve turn the game around and, just days after reaching the final of the Champions League, reinforce their position as Italy’s leading club with Inter left with work to do in their final two matches.
A seven-game unbeaten streak had taken Inter to within touching distance of a place in the Europa League next season and that positive trend looked set to continue when Icardi got the deftest of touches with his chest to Brozovic’s shot to divert the ball into the far corner of Marco Storari’s goal.
Rodrigo Palacio had a shot saved by Storari and Xherdan Shaqiri hit the crossbar with Brozovic’s goal on the rebound ruled out for a marginal offside decision as the hosts asserted themselves on the game.
Juve, fresh from booking their place in the final of the Champions League and with a changed starting XI, were not at the races until Alessandro Matri was put through on goal and he went down under the challenge of Nemanja Vidic just before half-time.
Marchisio stepped up to send Samir Handanovic the wrong way and bring the Bianconeri level.
Morata had two good chances to give Juve the lead early in the second half, but after shooting into the side-netting, he headed wide from a handful of yards out.
He did get his name on the scoresheet in the 83rd minute, but only thanks to a mistake by Handanovic, who let his weak shot slip through.
Inter could have levelled a few minutes later when both Palacio and Icardi were denied by Storari before Morata wasted a chance to seal things for the Italian champions, who are still on course for a treble after beating the first and last Italian side to succeed in that undertaking in 2010.