The Belgium midfielder scored the winner eight minutes before half-time to seal the points for Garcia's second-placed side, who made it five straight league games unbeaten on Saturday.
Roma made the better start to proceedings and came close to taking the lead after 18 minutes when Mattia Destro's shot from the edge of the box struck the post.
Chances proved few and far between after that missed opportunity, but the deadlock was finally broken after 37 minutes when Nainggolan, a recent arrival from Cagliari, struck.
The Belgium midfielder was presented with the simple task of turning into an empty net from point-blank range following excellent work from fellow midfielder Miralem Pjanic.
Bologna struggled in an attacking sense for much of the encounter but arguably deserved an equaliser after finishing strongly.
Defender Andrea Mantovani headed narrowly wide from a corner after 73 minutes as Roma began to ride their luck.
Greece midfielder Lazaros Christodoulopoulos was then presented with a gilt-edged chance in the final minute of injury time, but somehow managed to head substitute Davide Moscardelli's cross off target as Roma clung on to move within six points of leaders Juventus.
Manchester United eyeing surprise move for AC Milan star for whom tension in Italy is growing: report
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
