The hosts were ahead just over 10 minutes into the match as Alberto Paloschi picked out Riccardo Meggiorini with a long ball forward, leaving the latter to smash the ball in from just a couple of yards out.
Duje Cop had the best chance of the first half for the visitors when he controlled a lofted pass into the penalty area, but he rushed his shot, smashing it straight at Albano Bizzarri in the Chievo goal.
Despite the visitors seeing more of the ball at the start of the second half, it was the home side who had it in the back of the net with just over 15 minutes remaining, but Paloschi's strike was ruled out for an offside in the build-up.
Any hopes Cagliari had of finding a late equaliser were dealt a blow when Murru was given his marching orders for a dangerous tackle on Mariano Izco.
Pellissier could have added a second in stoppage time, but his strike from the middle of the box was saved, while Diego Farias had a chance blocked down the other end with just a few seconds remaining.
The result moves Chievo up to 12th in the table, while Cagliari remain in the relegation zone, eight points from safety.