After a slow start to 2018/2019, Inter looked like being frustrated again until Nainggolan produced a moment of quality in the 66th minute, netting with his side's first shot on target.
A muscular injury meant the former Roma midfielder's bow was delayed after his €38 million ($47.7 million) move, but it proved worth the wait for fans of the Nerazzurri.
Substitute Antonio Candreva and Ivan Perisic both struck inside the final eight minutes to wrap up a triumph that, while impressive, was not quite as comfortable as the scoreline suggests.
Having collected only one point from his first two games, the win comes as a timely boost to Spalletti, especially given it arrived without injured captain Mauro Icardi, who watched on from the stands.
A quiet first half only produced two significant chances, with Ivan Perisic unable to find the target at the far post after a second-minute Matteo Politano cross completely caught out home goalkeeper Lukasz Skorupski.
In denying Filip Helander at point-blank range at the other end, Samir Handanovic distinguished himself far better.
The Sweden defender appeared poised to apply the finishing touch when Danilo headed Erick Pulgar's cross into his path, only for the Inter keeper's reflexes to come to the rescue.
The game looked to be heading towards a goalless draw until Inter gradually upped the tempo after the break, a neat passing move seeing Politano find Nainggolan, who took one touch and buried a low strike into the bottom corner from 12 yards.
Federico Santander almost equalised for Bologna when he diverted his header inches wide from Federico Mattiello's threatening delivery, before Inter put the result beyond doubt.
Keita Balde Diao, who was standing in for Icardi in attack, blazed over a glorious late chance to put the game to bed after Danilo D'Ambrosio laid it on a plate for him, but Candreva made no mistake when he slotted in Perisic's delivery from six yards out.
Seventy-nine seconds later it was three, Perisic cutting inside Mattiello with a great dummy before lifting a fine finish over Skorupski.