Gattuso was taking charge of his first home game since being appointed as Vincenzo Montella's successor, and the Rossoneri wasted no time in gifting their new boss his maiden home goal at the helm when Giacomo Bonaventura broke the deadlock after just 10 minutes.
Simone Verdi levelled things up for the visitors midway through the first half, but a second from Bonaventura with less than 15 minutes remaining was enough to hand Milan their first win in four Serie A games and just their third maximum points haul from their last 11 outings.
The result lifts Milan up to seventh in the table and only three points off the European places, while Bologna remain in ninth place.
It was all too easy for the hosts to take the lead early on, with Nikola Kalinic getting on the end of a long ball forward and knocking it down into the path of Bonaventura, who swept his first-time finish past an unsighted Antonio Mirante from the edge of the area.
The lead lasted less than 15 minutes, though, and Bologna had their equaliser with a quarter of the match gone when Mattia Destro skipped past his marker on the left flank before cutting the ball back for Verdi, who improvised to lift a volleyed finish into the far corner.
Milan had the chance to react quickly when Franck Kessie beat a number of defenders on his way to the edge of the box, but his end product was disappointing and Mirante made a routine stop to keep the scores level.
Leonardo Bonucci was the next to come close for the hosts, who before tonight had been without a win or even a goal in their last four home league outings, but he nodded his header over the crossbar from a corner.
It was via the aerial route that Milan did eventually restore the lead in the final 15 minutes, though, as Bonaventura attacked Fabio Borini's cross aggressively to plant a towering header into the back of the net.
Bologna almost responded immediately when Saphir Taider's header needed to be saved by Gianluigi Donnarumma, and the Italy international was called into action again from the resulting corner when he tipped Adam Masina's effort over the top.
There was ultimately no way back for the visitors, though, as Milan held out for three valuable points which keeps them within touching distance of Sampdoria in sixth.
AC Milan (4-3-3): Donnarumma; Abate (Cutrone, 59'), Musacchio, Bonucci, Rodriguez; Kessie, Montolivo, Bonaventura; Suso, Kalinic (Andre Silva, 68'), Borini (Calabria, 83')
Bologna (4-3-3): Mirante; Torosidis, Gonzalez, Helander, Masina (Petkovic, 83'); Nagy (Taider, 64'), Pulgar, Donsah; Verdi, Destro, Palacio (Okwonkwo, 72')