Shola Ameobi fired Newcastle into the last 16 of the Europa League from the penalty spot as the Magpies kept their cool in icy Ukraine.
Ameobi's 15th European goal - only Alan Shearer has scored more for the club - came after midfielder Moussa Sissoko had been tripped by goalkeeper Olexandr Goryainov.
The striker calmly converted from 12 yards to silence a packed house at the Metalist Stadium in Kharkiv.
It was no more than the Magpies, who had two goals disallowed in last week's first leg on Tyneside, deserved from a spirited display, although goalkeeper Tim Krul, who had denied substitute Willian six minutes later, also had to pull off a stunning double save to keep out Jonathan Cristaldo 13 minutes from time.
Alan Pardew's men will now turn their attention to securing a second victory in four days when Southampton head for St James' Park in the Barclays Premier League on Sunday, but knowing they are safely through to the last 16 to face either Anzhi Makhachkala or Hannover.
Newcastle arrived knowing they needed to avoid defeat to at least take the tie into extra time, and that a score draw would send them through.
Pardew made five changes to the side which could only manage a 0-0 draw at St James', and that meant a debut for January signing Massadio Haidara at left-back and starts for Danny Simpson, Vurnon Anita, Sylvain Marveaux and Ameobi.
It was the visitors who made the brighter start as the physicality of Ameobi and Sissoko, as well as the control exerted by Yohan Cabaye and Anita in the middle of the field, caused all kinds of problems for the home side.
Ameobi saw a second-minute cross taken off Papiss Cisse's toe as he prepared to shoot after the former had left defender Marco Torsiglieri for dead wide on the left, and Sissoko might have opened the scoring with quarter of an hour played.
He controlled Cabaye's long ball out of defence superbly before cutting inside Torsiglieri, but his weak left-foot shot was easily fielded by Goryainov.
Ameobi's 23rd-minute flick-on caused panic in the Metalist defence once again, but the ball would not sit down for Cisse and it was eventually smuggled away.
The Magpies were enjoying much the better of the game as the temperature plummeted, and Goryainov had to punch away a Cabaye free-kick as Ameobi prepared to meet it at the far post three minutes later.
But the Ukrainians responded and went close twice within nine minutes through Cristaldo.
The striker headed inches wide from Cristian Villagra's 29th-minute cross, and then saw a 38th-minute effort from Jose Ernesto Sosa's corner blocked by defender Mapou Yanga-Mbiwa.
Newcastle could have gone in ahead at the break after Ameobi turned Sissoko's pass into the path of Cisse. The Senegal international had a clear run on goal, but just as he did on several occasions on Tyneside, 37-year-old Goryainov proved equal to the task to keep him at bay.
Both sides returned knowing a tense 45 minutes lay ahead, and it was Metalist who made the brighter start as they attempted to pressurise new boy Haidara.
Newcastle were careless in possession as the half got under way with Sissoko and Cisse gifting the ball to the hosts to stall any momentum, although midfielder Cleiton Xavier blazed a 53rd-minute free-kick high over, just as he had done during the first half, to let them off the hook.
However, Marveaux was just as profligate three minutes later when he exchanged passes with Sissoko, but blasted high over from a tight angle with a square ball perhaps the better option.
But the Magpies made the breakthrough with 26 minutes remaining when Sissoko's industry was finally rewarded.
The midfielder chased down a poor back-pass by defender Papa Gueye and in his efforts to rescue the situation, Goryainov tripped the Newcastle man.
Belgian referee Serge Gumienny pointed straight to the spot and after Sissoko had received treatment, Ameobi kept his nerve to send the goalkeeper the wrong way.
His strike was greeted by a deafening silence as the 500 travelling fans celebrated knowing their side had one foot in the last 16.
But if they needed a reminder that there was work still to be done, Krul had to come from his line to deny Willian with 20 minutes remaining as Myron Markevich's men launched a late assault.
The Dutchman excelled once again seven minutes later to prevent Cristaldo from levelling twice within seconds as Pardew's men held firm to secure the victory they wanted.