The Sardinians had slipped dangerously close to the Serie A drop zone in recent weeks but a 1-0 victory at the Stadio Sant'Elia saw them pull eight points clear of 18th-placed Livorno.
Verona, now in 10th, were the surprise package in the first half of the season and looked set to challenge for a Europa League place but have now failed to score or earn a point since February.
Andrea Mandorlini's Hellas were hammered 5-0 at Sampdoria on Sunday and decided to roll over once again.
Swedish schemer Sebastian Eriksson tried his luck before crossing for Nene, who headed just wide, and in the 29th minute Agim Ibraimi shaved paint off a post with a left-footed drive.
Two minutes later, Nene headed Francesco Pisano's cross beyond Rafael and into the net.
Eriksson continued to impress and almost saw Matias Vecino profit from his handy work when the Uruguayan controlled a cross on his chest before shooting wide from 15 yards.
Nene missed a chance to make it 2-0 before the break, which could not come soon enough for Verona.
The Brazilian striker went close again when play resumed and Victor Ibarbo clattered a post as Cagliari continued to turn the screw.
Rafael saved Nene's bullet header before Ibarbo scooped the ball just over the crossbar shortly after the hour mark.
There were 10 minutes remaining when Verona decided to have a go and Bosko Jankovic was unlucky not to hit the target with a solid header from Romulo's high cross to the penalty spot.
Three minutes into stoppage time, Mauricio Pinilla missed an opportunity to kill the game off from six yards, but Cagliari had done enough.