Thiago Ribeiro put the visitors ahead 10 minutes in and, after Lecce went close to an equaliser on several occasions, Davide Biondini made it 2-0 before the interval.
The hosts continued to press for the remainder of the game but were unable to find a way past goalkeeper Michael Agazzi.
The opener came when Andrea Cossu crossed from the left and Thiago Ribeiro fired home from 10 yards with his right foot.
Lecce immediately sought a response and Djamel Mesbah shot wide after being set up by Massimo Oddo.
David Di Michele laid the next chance on a plate for Ignacio Piatti, who failed to find the net from close range.
Di Michele and Oddo went close with free-kicks before Cossu's set-piece delivery at the other end was headed wide by Davide Astori.
Agazzi saved well from Juan Cuadrado's header before Cagliari doubled their lead in the 39th minute, Biondini converting Alessandro Agostini's left-wing cross.
Di Michele failed to make contact with a dangerous ball on the edge of the six-yard box and Cagliari then countered, Radja Nainggolan shooting wide after a swift break upfield.
Lecce coach Mario Zanotti introduced Christian Pasquato for Piatti at half-time and the substitute carried the home side's early attacks. His free-kick was well saved by Agazzi before a cross from Pasquato flashed across the six-yard box with nobody able to get the necessary touch.
Cossu's cross was volleyed wide by Daniele Conti but it was a rare Cagliari attack, and Daniele Corvia's run on goal was only halted by an offside flag after he was well found by Di Michele.
Corvia saw a header from a Cuadrado cross deflected wide and then nodded Oddo's cross just past the near post.
And Lecce must have known with two minutes remaining it was not to be their day when Andrea Bertolacci set up Cuadrado but he could not beat Agazzi and Di Michele missed a straightforward follow-up chance.