Four days after their two-year unbeaten home run was ended by Lazio, Juve were in more trouble when goalkeeper Gianluigi Buffon saved at foot of Gelson Martins but the ball hit Alex Sandro and went straight into the net.
Miralem Pjanic levelled with a superb free kick in the 29th minute and, just as Sporting seemed set to frustrate the hosts, Mario Mandzukic scored the winner with a superb diving header in the 84th minute.
Juventus have six points from three games in Group D, three behind leaders Barcelona, while Sporting are on three.
"It was a tough game and an important win. Now, we have to start improving," said Juventus defender Giorgio Chiellini. "We reacted well because this team has got personality."
Already fending off talk of a crisis after taking one point from their last two league games, Juventus got the worse possible start with a double mistake by Alex Sandro in the 12th minute.
The Brazilian first failed to cut out Bruno Fernandes' pass through the Juve defence, allowing Martins a clear run on goal. Buffon managed to block the ball at Martins' feet, only for it to hit Alex Sandro and ricochet into the net.
At that point, it looked as if Sporting might claim their first win in Italy at their 14th attempt but it turned out to be their only shot on target all evening.
Juve quickly regained control and, after several near misses, levelled in the 29th minute when Pjanic curled an exquisite free kick over the wall, leaving Sporting goalkeeper Rui Patricio rooted to the spot.
Sporting defended resolutely in the second half while at the other end, Bas Dost kept the Italians' defence occupied but without seriously troubling Buffon.
A draw seemed on the cards until Douglas Costa, who had just come on, whipped over a cross from the left and Mandzukic beat his marker to the ball to score with a diving header at the far post.
Sporting coach Jorge Jesus refused to throw in the towel.
"We're still not out of it because we're perfectly capable of winning against Juventus in Lisbon," he said. "The result was unfavourable but we weren't inferior to Juventus."
(Writing by Brian Homewood, editing by Pritha Sarkar)
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