Mirko Vucinic and Alessandro Matri were also on target for the champions, who moved up to 48 points, five clear of second-placed Lazio.
Lazio drew 2-2 at Palermo, leaving the Serie A strugglers second bottom on 16 points.
"We were missing loads of players who would usually start... and today was a demonstration that despite all the absentees... we depend on the idea of a team, not individuals," Juventus manager Antonio Conte said.
A wonder-strike from more than 30 metres from Pogba helped to break the deadlock in the 41st minute after the champions wasted a host of chances during the first half.
Emanuele Giaccherini, Arturo Vidal, Pogba and Leonardo Bonucci all saw opportunities go begging despite the fact Udinese barely ventured out of their own half.
It was left to teenager Pogba to calm Juve nerves with his second goal of the night, drilling a long range strike into the bottom right-hand corner of the net in the 66th minute.
"Let's not forget that Pogba is only 19-years-old, he needs experience and needs to challenged because he's a player who sometimes tries to do it all on his own," Conte said as he praised the teenager who excelled in the place of the injured Andrea Pirlo.
"If leaving Pogba out for the next match is a problem then I'm happy."
Six minutes later Vucinic, with his back to the goal, hooked a weak shot straight at Padelli, which the keeper spooned into the net.
Matri sealed the points in the 80th minute when he ended a swift counter-attack by collecting Vucinic's through ball to calmly slot home his fourth of the season.
Udinese coach Francesco Guidolin blamed himself for his team's shortcomings.
"We're not an amazing team but we're not as bad as we looked tonight, we hardly created anything, and that's not the fault of the defence, the attackers or the midfield," he said.
"If a team goes out on to the pitch and expresses itself like that then it's the fault of the manager, and let's leave it at that."
In Saturday's earlier game, a late Hernanes penalty helped Lazio to snatch a 2-2 draw at Palermo.
Sergio Floccari's deft header gave Vladimir Petkovic's side the lead in the 10th minute but after the Lazio striker had a second goal wrongly disallowed for offside in the 62nd minute, Palermo struck with two goals in a minute.
First Egidio Arevalo Rios snuck around the Lazio defence to tap in Andrea Dossena's low cross at the far post on 70 minutes, then Paulo Dybala latched on to a Fabrizio Miccoli pass across the six-yard box to snatch the lead.
However, the title challengers dusted themselves down and attacked Palermo, and six minutes before the end of a frantic second half the impressive Floccari was chopped down by Ezequiel Munoz in the area.
Hernanes comfortably slotted home the penalty and despite pushing forward, they failed to get the winner that would have piled on the pressure on Juventus.
