Francesco Totti got the Giallorossi back on level terms 10 minutes before half-time when he cancelled out Radja Nainggolan's early opener, but it was one-way traffic after the interval as a comical Mauro Goicoechea own goal and further strikes from Marco Sau and Francesco Pisano secured an emphatic away win before substitute Marquinho's late consolation.
The result was particularly sweet for the Rossoblu after the Eternal City club were awarded a 3-0 win without a ball being kicked in anger during September's ill-fated reverse fixture.
Cagliari took only three minutes to get their noses in front, Nainggolan diverting Sau's right-wing cross into the bottom-right corner after a swift counter-attack.
The Sardinians nearly went two up soon after but Goicoechea got down well at the feet of Thiago Ribeiro to thwart the Brazilian.
Totti's influence on the game began to grow as the half wore on, the former Italy playmaker setting up Erik Lamela - who headed over the bar - before seeing a low cross cleared.
Sau then lashed just wide from close range as the hosts continued to push for the equaliser, and they did not have to wait too long.
Alessandro Florenzi teed up Totti, who slotted his shot coolly into the bottom-left corner.
Totti could have put his side in front before the break but fired over following good work by Lamela.
That miss proved costly soon after the restart, when Cagliari were gifted the lead thanks to an incredible mistake by Goicoechea. The Roma goalkeeper attempted to catch Danilo Avelar's cross but allowed the ball to slip from his hands and into the net.
Goicoechea tried to make amends with a decent save from Sau six minutes later, but he was beaten again in the 53rd minute when Sau headed Victor Ibarbo's right-wing cross into the top-right corner.
Totti continued to look Roma's best hope of getting back into the game, his shot just before the hour looking destined for the top corner before Cagliari goalkeeper Michael Agazzi's timely intervention.
But Cagliari too were still pressing and served warning they were not done yet when Ribeiro drilled a 25-yard shot against the post following another neat counter-attack.
They made it 4-1 19 minutes from time when Pisano pounced on the rebound after Sau had cut inside Marquinho and fired a shot against the post.
Ivan Piris, Pablo Osvaldo and Dodo all had chances to get Roma back into the game in the closing stages, but they could not find a way past Agazzi for a second time until the 93rd minute. Lamela set up Marquinho, whose effort from the edge of the box found the bottom-right corner, but it was too little too late for the hosts.