Alan Pardew's side were the first team to threaten as Yohan Cabaye lifted a over the Metalist defence for Moussa Sissoko but his tame effort was saved.
Just before the break, Papiss Cisse missed a great chance to give his side the lead as the ball fell to him inside the area but he shot straight at Oleksandr Goryainov.
After the break, Newcastle took the lead from the penalty spot following a catastrophic error from Papa Gueye as miscued his back-pass to Goryainov, allowing Sissoko to pounce.
Goryainov then brought down the midfielder inside the penalty area allowing Ameobi to score from the spot, blasting the ball into the top corner.
The home side almost responded straight away as Willian was presented with a great chance inside the box but Krul was equal to his effort when he tried to lift it over the Dutchman.
Newcastle were indebted to Krul again as he made a double save to deny Cristaldo, first blocking his shot with his body and following a scramble in the area, he made a great reaction stop to parry his goalbound effort away from the net.
Willian came close to getting his side level but was denied yet again by Krul, who pulled off another reaction stop to keep his header at bay from a corner, which was enough to secure the win.