Colombian Bacca, signed from Sevilla last month, outran two defenders to score in the 16th minute at the San Siro.
Former Milan player Riccardo Saponara equalised for Empoli four minutes later, sliding the ball under the legs of goalkeeper Diego Lopez.
Brazilian Luiz Adriano, sold by Shakhtar Donetsk for eight million euros (£5.76 million), then headed the winner in the 69th minute as Milan moved into 10th place after two matches.
Striker Mario Balotelli, back on loan at his old club from Liverpool, was greeted with a few whistles when the Milan names were read out and spent the game on the bench.
Sassuolo substitute Floro Flores brought a dull game to life at Bologna by scoring four minutes from time, his second goal in as many games.
The 1-0 win allowed Sassuolo to go top of the table, at least until Sunday when a busy programme of games includes champions Juventus travelling to AS Roma.
Juve and Roma have finished first and second respectively in each of the last two seasons.
(Writing by Clare Fallon; Editing by Tony Jimenez)
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