Lazio did just about enough to push past Bologna with Pedro setting up the tap-in for Felipe Anderson after an emotional tribute to Sinisa Mihajlovic.
The winners go on to face either Juventus or Monza in the quarter-final of the Coppa Italia.
There were emotional scenes before kick-off, as Mihajlovic’s wife Arianna and their children watched a video tribute on the touchline before saluting the supporters with the jerseys representing his career at the two clubs as player and coach.
Ciro Immobile was out with a thigh strain, while Bologna missed Marko Arnautovic, Nicola Sansone, Kevin Bonifazi and Lorenzo De Silvestri.
The hosts almost scored in the opening 15 seconds, Felipe Anderson sent clear on goal only to fire straight at the goalkeeper.
Sergej Milinkovic-Savic nodded a corner just off target and Mattia Zaccagni tested Lukasz Skorupski, then Joaquin Sosa risked an own goal with his clumsy clearance on Pedro’s free kick.
Bologna shot themselves in the foot with a howler for the opening goal, as Sosa was caught napping by the high Pedro press, pulled back from the right for Felipe Anderson to simply tap in from close range.
Riccardo Orsolini chested down a Jerdy Schouten ball over the top only to then shin the finish, while Milinkovic-Savic soared to meet a Zaccagni cross only to nod it over the bar from four yards.
Luis Alberto’s volley was scuffed at Lukasz Skorupski and Bologna lost Gary Medel to a knock just 25 minutes after his introduction.
Lazio 1-0 Bologna
Felipe Anderson 33 (L)