In a game short on quality, two fine goals in either half kept the Giallorossi's title hopes alive as they claimed their first league victory since January 6
Rudi Garcia's side had seen themselves fall 10 points behind Juventus on Saturday following the champions' win over AC Milan, with a series of draws scuppering their hopes of maintaining a title charge.
However, Ljajic's prodded finish - set up by a delightful chipped pass from Verde - gave Roma the lead in a scrappy first half, and Paredes sealed the win through a fine effort in the closing stages, with a stoppage-time goal from Paul-Jose M'Poku coming too late for Gianfranco Zola's men.
It was Verde who came closest for Roma in the first half-hour as he raced clear through the centre of the area, but he could only sidefoot inches wide of the near post.
At the other end, Duje Cop called Morgan De Sanctis in to action with a shot from the edge of the area as Cagliari pressed Roma high up across the pitch, though chances remained few and far between for much of the half.
However, Roma took the lead shortly before the interval, with the impressive Verde clipping a clever ball over the top and into the path of Ljajic, who stabbed home into the roof of the net.
Cop came close again for Cagliari, forcing De Sanctis to parry his effort from Joao Pedro's knockdown, before wasting a golden chance to level following Mapou Yanga-Mbiwa's failure to clear, when he could only fire over the crossbar when clean through.
And Roma made them pay on the break in the closing stages, with Verde firing in a cross from the left which was met with a brilliant strike from substitute Paredes.
Mpoko climbed highest to power home a cross from Danilo Avelar in stoppage time, but it was too little too late for Cagliari.