The 20-year-old Slovenia international struck 21 minutes into the second leg of the club's play-off clash with Greek side Atromitos to seal a 2-1 aggregate victory.
However, although Alan Pardew's men dominated on the night, they were unable to kill the tie off before the final whistle and enjoyed a major escape when goalkeeper Tim Krul appeared to fell Chumbinho in the box two minutes before the break, only to see the Brazilian midfielder pick up a booking for diving.
Had it not been for the excellence of Atromitos keeper Charles Itandje, who at times was left to repel Newcastle single-handedly, the home side's place in tomorrow's draw in Monaco would have been assured long before the game drew to a close.
In the event, the first European fixture on Tyneside since March 2007 ended in victory for the Magpies and booked an extended stay in the tournament.
Pardew was confident enough to use only four of the men who started at Chelsea on Saturday evening - Krul, Fabricio Coloccini, Danny Simpson and Demba Ba - with one eye on Sunday's Barclays Premier League clash with Aston Villa, and his faith appeared to be well-founded before the break.
With wide-men Gabriel Obertan and Sylvain Marveaux tormenting full-backs Konstantinos Giannoulis and Ioannis Skondras respectively, the Magpies were on the front foot from the off despite losing Ryan Taylor through injury with just 11 minutes gone.
Taylor's departure - he collapsed in agony after challenging for a ball on the touchline and after treatment was helped down the tunnel - saw James Perch drop in at left-back to accommodate Vuckic in the middle of the field.
The youngster needed just 10 minutes to make his mark, turning smartly on to Simpson's throw-in before lashing a left-foot shot past Itandje with the help of a slight deflection from 22 yards.
Marveaux had earlier tested the keeper with a well-struck effort after surging into the box from the left, and Itandje found himself in the thick of the action as the half wore on.
He produced a fine one-handed save after Ba's 27th-minute attempt had taken a much more substantial deflection on its way to goal, and was relieved to see Obertan's strike fly wide with the help of a touch off a defender seven minutes before the break.
The traffic was largely heading towards Itandje's goal with opposite number Krul having only to mop up occasionally as lone Atromitos frontman Tasos Karamanos was left isolated with his midfielders battling manfully to stem the tide.
However, the visitors might have been back in the game and the tie two minutes before the break after Krul gave them hope.
The Holland international made a mess of dealing with Denis Epstein's long-range shot and when Chumbinho attempted to collect the rebound, appeared to bring him down.
Swiss referee Stephan Studer blew immediately, but instead of pointing to the spot, he booked the midfielder for diving much to the player's astonishment.
Obertan might have extended Newcastle's lead within seconds of the restart after being played in by Ba, but once again Itandje did just enough to deny him.
The keeper did not need to be at his best to field Ba's ambitious 30-yarder, and Krul and his defenders were happy to see the flag go up seconds later as Chumbinho collected Brito's long ball and finished with some aplomb.
With the game entering its final 30 minutes and the Magpies yet to end it as a contest, the Greeks made their final push, committing men to the search for an equaliser which would take the tie into extra-time.
Coloccini headed Gael Bigirimana's 66th-minute free-kick high over as Newcastle responded, but there was a growing sense of unease around the stadium.
Marveaux wasted a two against two break when he failed either to get a shot away or find team-mate Ba, but Obertan should really have put the result beyond doubt when he broke clear with 19 minutes remaining, but again could not beat Itandje.
Karamanos fired high over Krul's goal, but Elini Dimoutsos was even more wasteful 11 minutes from time when he dragged a shot across goal with only Krul to beat.
Epstein blasted inches over the top in injury-time, but there was no way back for Dusan Bajevic's battlers.