Second-half heroics from Tim Krul helped Alan Pardew's side progress to the last 16 after the home side gifted the Magpies a penalty in the second half that sealed the tie.
Shola Ameobi scored the vital goal for the Magpies from the penalty spot after a mix up between Papa Gueye and Olexandr Goryainov.
The home side was unchanged from the draw at St James' Park, while Alan Pardew made four changes to last week's lineup. Danny Simpson and Massadio Haidara came into the defense for Steven Taylor and Davide Santon, with Mapou Yanga-Mbiwa switching from right back to center back and Haidara making his debut for the Magpies.
Elsewhere, Cheikh Tiote was ruled out with Vurnon Anita replacing him in the side, and Sylvain Marveaux came in with Jonas Gutierrez dropping to the bench.
The first real moment of danger came after 15 minutes when Moussa Sissoko embarked on a run down the right wing before cutting in, but the placed effort on his left-foot lacked conviction and rolled harmlessly to Goryainov in goal.
Ameobi then managed to work enough space on the edge of the box to get a shot away, but his left-footed drive was deflected wide past a stumbling Goryainov.
Metalist had its first chance after 28 minutes, as striker Jonathan Cristaldo headed narrowly wide of Tim Krul's post, with the right flank becoming the club's main focus of attack. The Argentine then had a free header from a corner 10 minutes before the break, but made a mess of his attempt.
With five minutes left of the first half, Papiss Cisse had his first effort, finding himself in space to receive the ball from Ameobi, but his effort was straight at Goryainov.
Neither side dominated the first half, with referee Serge Gumienny frequently stopping play, penalizing 24 fouls in the first 45 minutes.
Ten minutes into the second half, the Newcastle should have taken the lead. Marveaux was played in down the left side of the penalty area, but rather than square it to the unmarked Ameobi or Cisse, the Frenchman crashed an effort over the bar, much to his teammates' disapproval.
In the 64th minute, Newcastle finally made the breakthrough with a gift of a penalty after a mix-up between Papa Gueye and Goryainov. The defender over hit a back pass, with Sissoko capitalizing and being brought down by the goalkeeper.
Ameobi stepped up and swept the ball to the keeper's right, sending him the wrong way and leaving Metalist needing two goals to progress.
Five minutes later, Krul made a vital stop as substitute Willian found himself through on goal within seconds of coming on, but his attempted dink was blocked by the keeper.
The Dutchman was called upon again in the 77th minute, making three stops in a matter of seconds. Cristaldo was through, but his shot was straight at the keeper. From the rebound he pushed out a cross-shot, and then Cristaldo was on hand again to turn a wayward shot goalwards, with Krul making another fine stop, springing away to his left.
With five minutes to go, Willian's header forced another great save from Krul, keeping the ball out with the help of his post.
Despite the danger, Newcastle held on to progress through to the final 16 of the competition.