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 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 Premier League on Sunday, but knowing they are safely through to the last 16 to face either Anzhi Makhachkala.