The Belgian midfielder, who is reportedly interesting the likes of Chelsea and Manchester United, put Roma into the lead midway through the first half before Antonio Rudiger doubled up six minutes before half-time. Miralem Pjanic rounded off a 3-0 win with five minutes remaining.
Luciano Spalletti's men can be dislodged from second - the route of direct entry into the UEFA Champions League group stage - by Napoli when the Azzurri visit Torino.
With rumours swirling that Nainggolan is poised to make a northern summer switch to the English Premier League, it was fitting that the playmaker stole the show at the Stadio Olimpico, thus putting himself firmly in the shop window.
The former Cagliari player forced a solid save from Albano Bizzarri when laying into Lucas Digne's pass and, after Lucas Castro had tried his luck at the other end, Nainggolan did open the scoring.
With 18 minutes gone he played a clever one-two with the rapid Mohamed Salah before shaking off a challenge from Bostjan Cesar to slot the ball home without too much effort.
Chievo were rattled but recovered well to get Wojciech Szczesny working when Paul-Jose M'Poku found Antonio Floro Flores for an angled drive that looked destined for the far corner until Roma's Polish goalkeeper intervened.
At the other end, Pjanic fizzed the ball just past a post before Roma doubled up through an unlikely source in the 39th minute.
On-loan Stuttgart defender Rudiger rose highest to meet Pjanic's lofted free-kick, the German nodding it beyond Bizzarri for his second goal of the season.
Chievo could have slashed the deficit heading into half-time but Floro Flores' snapshot was not potent enough to beat Szczesny in stoppage time.
The Flying Donkeys, who secured their top-flight status weeks ago, seemed more relaxed after the break and the lack of pressure allowed them to rattle Roma twice before the hour mark.
First, Gennaro Sardo nodded a Nicola Rigoni free-kick inches wide, and M'Poku then clattered a post from close range when Szczesny was stranded.
Applause rang around the ground as Francesco Totti took to the pitch. The 39-year-old was making his 600th Serie A appearance and soon put Alessandro Florenzi through with a cute pass that the rampaging full-back failed to make the most of.
Chievo were unfazed, though, and Floro Flores blasted wide before Sergio Pellissier sent Szczesny sprawling with a header from Fabrizio Cacciatore's cross.
The Giallorossi finally broke out of their despondency in the 78th minute when Stephan El Shaarawy collected the ball on the edge of the area before eliciting a remarkable diving save from Chievo stopper Bizzarri.
There was time for Totti to make yet another positive contribution to the team he has played for since 1993. In the 85th minute the veteran forward slipped Pjanic into a one-on-one with Bizzarri and the Bosnian schemer could not miss.