The visitors rode their luck as Buffon turned another effort by the Chilean around the post and Daniele Conti headed over the bar.
It put the Serie A leaders in danger of losing at last after a sequence of ten consecutive victories, but Fernando Llorente equalised when he headed in Stephan Lichtsteiner's cross in the 31st minute, then Buffon made another outstanding save to block Daniele Dessena's diving header.
Juventus settled the game in the last 20 minutes when Claudio Marchisio - who, along with Davide Astori, was one of the players Moyes is reportedly scouting - came off the bench to score a 30-yard stunner, with Llorente finishing off a counter-attack for the third goal and Lichtsteiner pouncing on a blunder by goalkeeper Adrian Adan for the fourth that turned a tough trip into a comfortable victory - a club record 11th on the trot.
It was all too much for Pinilla, who was sent off for dissent.
At the halfway point in the championship, Juventus have 52 points from 19 games, Roma 44 and Napoli 42, while Fiorentina, still waiting for striker Mario Gomez to recover from a knee injury, are a further five behind in fourth.
Antonio Conte praised Juventus for their "extraordinary achievement” of an 11th straight win in Cagliari.
“It’s an extraordinary achievement, the fact in the history of Juventus – knowing the teams they had – never managed this before is amazing. The lads deserve applause, as football can go so quickly that you barely have time to enjoy these moments," he said.
“Now we want to continue this positive streak, knowing full well there will be teams lining up to stop us.
“Our start wasn’t that bad, but we conceded on the first opportunity and risked again on another set play. These are distractions we rarely allow ourselves.
"I called the team to get their minds on the job, as the mind leads the legs.
“Even in moments of difficulty, we held out well and forced Cagliari to use up their energy with a very strong opening hour. This team held Roma at the Olimpico, which shows how good they are.
“Claudio [Marchisio] is an important player for us and I must thank him for his professional attitude, he’s a real champion. He has ended up on the bench this season, but behaved like a great champion and has Juve in his heart.
"You can see he’s in good shape and today I needed a change of pace in midfield, which he provided.
“Pirlo is coming off a serious injury and is training intensely, so it’s inevitable he’ll have dips in form during the game. I am fortunate enough to have Claudio and others on the bench ready to come in.
“I try to do my best as a Coach and when I make substitutions I look everyone up and down fully before choosing my players. I don’t look at the names or the faces first. I just try to pick the best available team. Sometimes I get it wrong, others I make the right choice.”
Juventus's closest rivals also won, with Roma thrashing Genoa 4-0 and Napoli winning 3-0 away at fifth-placed Verona.
Elsewhere, Parma beat Livorno 3-0 and Atalanta edged Catania 2-1, while both Bologna v Lazio and Torino v Fiorentina ended in goalless draws.