Dusan Vlahovic netted his first goal of the campaign as a starter, having scored four after coming off the bench with a fifth-minute spot-kick, It was cancelled out in first-half stoppage time by Nicolo Zaniolo.
Federico Gatti added to their tally on 67 minutes, with Kenan Yildiz slotting in the third for a convincing and rare win. The Allianz Stadium experienced excitement, drama and goals on Wednesday night.
Following the aftermath of Igor Tudor being axed following an eight-match winless streak and failing to score in four games, interim manager Massimo Brambilla shook things up with an attack-minded line-up.
Juventus came out of the traps with former Bianconeri target Saba Goglichidze conceded a penalty after fouling Vlahovic on three minutes. The Serbia striker dusted himself down and just under 100 seconds slotted past keeper Maduka Okeye and into the bottom left corner.
After Juve's recent toothless displays, and timid attempts at scoring, this strike got the team firing on all cyclinders with waves of attacks. The visitors looked, for most of the first half, like rabbits caught in the headlights.
Vlahovic set up Openda on 10 minutes, but Openda was unable to bag his first goal in a Juve jersey from the edge of the area by guiding his effort narrowly wide of the target.
The offside trap caught out Vlahovic and McKennie before Hassane Kamara skied his shot from a corner midway through the opening half.
Vlahovic showed swagger, but headed Filip Kostic's cross following a corner just after the half-hour mark, and 10 minutes later forced a save from Oyoye. The shotstopper who denied Locatelli's tame close-range effort before preventing Vlahovic's drive from finding the bottom left.
With Juve dictating the opening half, they were surprisingly pegged back in the first minute of added time when Zaniolo's left-footer from the centre of the box beat Di Gregorio shot into the bottom left corner to silence the majority of home supporters.
Defender Goglichidze went hell for leather, having one effort saved and another blocked, to lift an average looking Udinese sides, immediately after the turnaround.
This jolted Juventus but Locatelli and McKennie wasted glorious chances to restore the lead, followed by Openda drawing another save from impressive shotstopper Okoye on the hour-mark.
With the home supporters willing on the battling Bianconeri it became one-way traffic. Overworked Okeye denied Vlahovic and Pierre Kalulu but could not prevent Gatti from heading home Andrea Cambiaso's cross following a corner.
Ten minutes after regaining the lead luckless Openda was replaced by out-of-form David, and within 60 seconds of the Canada striker's arrival Turkish talent Yildiz struck the left upright from long range.
With Brambilla's late changes to shut up shop almost backfired when Vakoun Bayo was given space in the box but directed his 90th-minute header to the right of the gaping goalmouth.
With the contest looking to peter out Goglichidze conceded a second spot-kick, fouling Yildiz who made no mistake by drilling the penalty into the bottom left corner six minutes into added time.
The Allianz Stadium erupted at the final whistle, with the home fans having patiently waited for a performance worthy of Juventus. It was an well-worked first-half but after the interval the result could have gone either way with box-to-box action.
While Brambilla secured the first win for Juve since mid-September's dramatic Derby d'Italia triumph, Udinese manager continued his unwanted record of having failed to secure a midweek success since he was appointed last year.
This was a vital confidence-boosting win for Juventus, and with Vlahovic getting the sort of service he warrants could kick off a new era.
JUVENTUS: Di Gregorio - Kelly, Gatti, Kalulu - Locatelli - Kostic (Rugani, 89), Yildiz, McKennie, Cambiaso - Vlahovic (Koopmeiners), Openda (David, 77). Subs: Perin, Conceicao, Zhegrova, Adzic, Miretti, Rugani, Mario, Felipe, Mangiapoco