Wolves had won each of their previous three outings in all competitions and looked full of confidence early on, but were stunned in the 14th minute when the Magpies broke swiftly through Gordon.
He fed Bruno and while the Brazilian's left-footed shot was deflected, Isak adjusted quickly to head home at the Gallowgate End.
Five minutes later, United counter-attacked incisively once more and Dan Burn - making an adventurous surge forward in support - flashed a strike across goal.
The visitors came close when Toti sent a header off target, then Isak and Jacob Murphy both had efforts held by Jose Sá.
But, with rain pouring from the sky above St. James' Park, the Wolves goalkeeper was unable to hold Murphy's right-wing cross in the 33rd minute, and Gordon followed up to score his tenth goal of the season in all competitions.
Murphy sent a 25-yard effort over the bar two minutes later, but United deservedly led at the break.
Ten minutes into the second half, Gordon found the overlapping Burn with a backheel and Burn dug out a wonderful cross which was met by a diving header from Joe Willock. However, Toti was able to clear off the line.
Jeanricner Bellegarde fired over for the visitors from just inside the box in the 64th minute, then substitute Nathan Fraser brought a good save from Martin Dúbravka.
In the 68th minute, United were again grateful to their goalkeeper as he denied Pablo Sarabia at his near post, and Dúbravka made another flying save to hold Bellegarde's powerful header, with the Slovakian shot-stopper fully earning his clean sheet.
But Newcastle ended the game on top. In the 79th minute, following some ridiculous skill and a perfect pass from Bruno Guimarães, substitute Miguel Almirón was denied by Daniel Bentley - a half-time replacement for Sá.
Then Guimarães came close with a 22-yard strike which whistled just wide, before, in added time, Livramento dribbled into the box and netted his first goal for the club.
Only the injury to Kieran Trippier which saw Livramento replace him early in the second half threatened to dampen spirits on a generally damp day, but Newcastle were back to winning way at St. James' Park as they overtook their opponents in the Premier League table.
