Pinilla won the spot-kick in the 65th minute but then shot over from 12 yards.
Chievo, dwelling just above the relegation zone after their 16th point of the season, even had the chance to snatch all three but Alberto Paloschi's glaring late miss meant the points were shared.
The first half was a lacklustre affair, though Pinilla saw an early shot saved by Chievo keeper Christian Puggioni.
Free-kicks provided the clearest sights of goal up until the break, with Chievo's Luca Rigoni heading Cyril Thereau's delivery just wide.
Cagliari threatened when Davide Astori's set-piece picked out Andrea Cossu, who shot over, while Thereau went directly for goal from his next free-kick but keeper Antonio Adan punched the ball away.
A cross-shot from Chievo's Simone Bentivoglio shortly before half-time was wayward as both teams failed to break the deadlock.
The second half started slowly but Thereau went close from Perparim Hetemaj's cut-back, his shot skimming the right-hand post on its way out of play.
Albin Ekdal went close for Cagliari before Bostjan Cesar presented them with their best opportunity.
The Slovenia defender fouled Pinilla in the box and the forward picked himself up to take the kick himself, but got underneath his effort and failed to test Puggioni.
Davide Astori headed Matias Cabrera's corner over as Cagliari missed out on victory.
And they were almost punished even more severely as the impressive Thereau crossed from the left and picked out Paloschi, who failed to tap the ball in from close range.