An assured start from the away side prevented Metalist from imposing their own game and a composed penalty from Shola Ameobi ensured that they took the lead in the second half.
While the home team kept knocking on the door, Newcastle goalkeeper Tim Krul managed to dispel any threat from the Ukrainian outfit to book a tie against Anzhi Makhachkala or Hannover.
He told the club's official website: "The atmosphere will probably be the first time we really experience a hostile crowd in this competition.
"But we have players who have played on the international stage and are used to that scenario, so I don't envisage a problem. If I put my best team up against any team in this competition, I would feel confident."
"As I said after the first game, Newcastle are a very good team and they shouldn't be in the position they are in," BBC Sport quotes the manager as saying. "They should be in the top 10 minimum."
"Papiss is pretty easy-going and he knows he is going to get chances playing in this team," BBC Sport quotes Ameobi as saying. "With the players he has got behind him feeding, he is going to get chances to score goals, and hopefully he can do that on Thursday.
"When he gets on a roll, there's no stopping him, so hopefully he can keep getting into those positions and he can start banging them away."