The only goal of the tie came after 64 minutes when Papa Gueye's woeful back-pass was seized upon by Moussa Sissoko before he was brought crashing to the ground by Aleksandr Goryainov.
That allowed Ameobi to slot home his 15th European goal - only Alan Shearer has scored more for the club, as the Metalist goalkeeper dived the wrong way.
Magpies' Tim Krul then produced a string of spectacular saves to deny the hosts a way back into the tie as Alan Pardew's men advanced to the next stage of the competiton and a clash against Russian giants Anzhi Makhachkala.
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 Vurnon 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.
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.
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.
|Metalist Kharkiv||Team Statistics||Newcastle United|
|0||1st Half Goals||0|
|5||Shots on Target||3|
|8||Shots off Target||3|
|45.9||1st Half Poss.||54.1|
|65.8||2nd Half Poss.||34.2|