Defender Stephan Lichtsteiner returned after almost two months out with an injury and he was instrumental in the Juventus goal flicking on a cross for Llorente to head past the motionless Zeljko Brkic.
Llorente had almost scored moments earlier but saw his header cleared off the line by Udinese defender Allan.
Kickoff had been brought forward to allow more than 12,000 children to fill the stands behind each goal, replacing the ultras which had been banned for insulting territorial chants against Napoli.
It was Juve's sixth successive league victory without conceding a goal.
"We have to continue like this," Juventus coach Antonio Conte said. "We have 12 wins, a draw and a defeat. That's very important but we mustn't sit back on our successes.
"We were good today and lucky. We played well and showed that we are doing well physically, despite playing three games in a week. Buffon was good today, but Brkick was exceptional."
Key playmaker Andrea Pirlo limped off after 13 minutes with a knee injury.
Earlier, Roma was held to its fourth successive draw.
Atalanta, which had hit the post in the first half, took the lead seven minutes after halftime when Davide Brivio sent a free kick under the wall and into the bottom right corner, although Roma goalkeeper Morgan De Sanctis was partly at fault as he misjudged the ball.
United States forward Michael Bradley thought he had leveled in the 76th but his header was harshly ruled out for offside.
Atalanta goalkeeper Andrea Consigli made several good saves, but could do nothing when Adem Ljajic crossed for Kevin Strootman to tap in from six yards.
There was also a last-gasp leveler at San Siro, where Thohir was watching his first match since being elected president last month. Inter captain Javier Zanetti made his first start since snapping his Achilles tendon in April.
Inter took the lead in the 18th when Ricardo Alvarez worked his way through on the left of the area before rolling across for Fredy Guarin to lash in under the bar.
Guarin almost doubled his tally seven minutes after the interval but his effort crashed off the post. Shortly afterwards Sampdoria striker Nicola Pozzi's effort was ruled out for offside.
Substitute Renan leveled in the final minute, with a powerful shot from distance, just three minutes after coming off the bench.
"This was our worst performance of the season," Inter coach Walter Mazzarri said. "We went too deep after going 1-0 up and we didn't even start well. Too many were under par and Sampdoria deserved the draw.
"I didn't like this Inter. We should never let our guard down."
In the lunchtime kickoff, Milan dominated possession but it was Catania that took the lead in the 13th against the run of play as poor defending eventually saw Lucas Castro's effort deflected over stand-in goalkeeper Gabriel.
The visitors leveled six minutes later when Riccardo Montolivo volleyed Urby Emanuelson's cross into the back of the net.
Balotelli had gone six matches in all competitions without a goal before Tuesday's 3-0 win at Celtic, but he was involved in most Milan moves and fired his side in front shortly after the hour mark with a low free kick.
Moments later Catania were down to 10 men when Panagiotis Tachtsidis was harshly shown a straight red for a challenge on Balotelli.
Kaka sealed the match nine minutes from time, bursting into the box and firing into the roof of the net from a tight angle to score for the third successive match. It was his 99th Milan goal.
Milan moved provisionally level with eighth-placed Lazio. Catania remains at the bottom of the league.
There was another positive for Milan as Stephan El Shaarawy made his return from injury, coming on in the 74th for his first appearance in three months.
Balotelli was replaced seven minutes from time after getting into a heated argument with Catania defender Nicolas Spolli, whom he accused of racism.
"I didn't hear anything, so I can't judge," Milan coach Massimiliano Allegri said. "I took Mario off only because I saw he was a bit tired and had taken some knocks. There are so many skirmishes on the pitch, in any match, what's important is to stay calm."
