The attacker's late third capped off the win nicely, after first-half goals from Mattia Destro and Kevin Strootman set the tone as the home side dominated throughout.
In truth, the score could and should have been significantly higher as Rudi Garcia's men were denied by Francesco Bardi's numerous saves and their own intermittent profligacy as they attacked relentlessly at the Stadio Olimpico.
Mattia Destro gave the Giallorossi an early lead in controversial circumstances, as Gervinho was offside when the ball flicked off him for the striker.
Kevin Strootman then finished off a fine attacking move with a flourish, hammering in from close-range, with the Amaranto lucky to be only two goals down at the break.
The visiting side was lifeless and showed no signs of inspiring a comeback and Adem Ljajic capped off the night by curling in from the edge of the box with less than 15 minutes to go.
The victory for second-placed Roma keeps Juventus within sight at the top of the table, while Livorno's fifth-straight defeat sees the club remain four points adrift of Serie A safety and rooted to 19th.
Attilio Perotti's first game in charge in his promoted role of head coach turned sour in less than six minutes.
Destro, fully integrated back into the Roma side after his long spell out injured earlier this season, converted Ljajic's fizzing cross, though it deflected off Gervinho who was evidently offside when the ball was played across goal.
The home team kept the pressure piled on. Daniele De Rossi slid in an incisive through ball for Destro, but Bardi came off his line to deny the forward a second goal.
Bardi was again the savior with 30 minutes gone as Gervinho's strike from 10 yards was saved by the Livorno shot-stopper after Miralem Pjanic's fine pass for the Ivorian.
But in the 36th minute Bardi could not hold back the floodgates any longer. Dodo's deft chip over the goalkeeper to the left of the goal was whacked in with venom by Strootman to double the lead.
Vasilis Torosidis' first-time cross should have been converted into a third Roma goal but Gervinho - who put in a vibrant performance at the Stadio Olimpico - somehow nodded it wide unmarked six yards from goal.
Garcia's men thought they had scored a third on the brink of halftime but the goal was correctly ruled out as Leandro Castan - offside when Destro fired in - was blocking Bardi's view as he hopped over the goal-bound ball.
Livorno seemed content to sit back and take the beating, even after the break, with the Giallorossi attacking over and over without suffering on the counterattack like they might have done against better opposition.
Although it was mostly Bardi who Perotti could thank for not conceding double figures, Ibrahima Mbaye did well to block Pjanic from firing in a third for the home side.
With 15 minutes left on the clock, substitute Radja Nainggolan's gorgeous flick-on saw Ljajic sprint through but once again he was denied in an one-on-one situation.
But three minutes later a similar link-up ended in a third strike of the night. Nainggolan passed to Ljajic who curled his effort into the near post with aplomb from 20 yards out to finish Roma's night off in style.