In a first half that Wolves controlled, without being spectacular against a poor visiting side, the opening goal was created wonderfully by Raul Jimenez and neatly finished by Hwang.
But the Magpies equalised before half time with a controversial Jeff Hendrick striker as goalkeeper Jose Sa lay injured on the floor.
The second half was fairly flat from the hosts but some magic once again from Jimenez set up Hwang for his second against the run of play.
From there it was a tough battle as Newcastle tried desperately to get back into the game, but Wolves stood firm to back it back-to-back Premier League wins and their first at home this campaign.
Bruno Lage made two changes to his starting XI and stuck with the 3-4-3 formation.
Ruben Neves and Francisco Trincao came in to replace Leander Dendoncker and Daniel Podence, as Adama Traore was again left on the bench.
Rayan Ait-Nouri came back into the squad after missing the Southampton fixture with concussion, and was among the substitutes. Youngster Luke Cundle also made the bench as Yerson Mosquera, Pedro Neto and Jonny Casto Otto missed out through injury.
Steve Bruce named an unchanged side following Newcastle’s 1-1 draw with Watford last week, starting in a 4-1-4-1 formation.
Influential players Callum Wilson and Jamaal Lascelles were unavailable through injury, but star forward Allan Saint-Maximin started.
Under cold and wet conditions at Molineux, Wolves struggled to get going in the opening minutes in what was a very stop-start game. That was mainly due to Lage’s side giving away too many free-kicks early on. Fortunately, none of them were punished by Newcastle.
Hwang got fans off their seats when he intercepted the ball in midfield, beautifully nutmegged one Newcastle player before releasing Jimenez down the left flank. The South Korean made a run forward to receive the ball back but the chance fizzled out.
But after 20 minutes the pair did combine for the opening goal. Jimenez showed superb determination to ride a challenge in midfield and race towards goal before slotting a lovely through ball for Hwang. The forward neatly finished beyond Karl Darlow to send Molineux into raptures.
Following the goal, Wolves had their tails up and looked dangerous every time they went forward. Newcastle sat back in their defensive shape to try and absorb the pressure, tasking the home side to break them down. A decent effort from Joao Moutinho from 25 yards forced Darlow into a save, too.
A few misplaced passes from Wolves allowed Newcastle some half chances that were not taken, before the hosts should have made it 2-0. Hwang was released by Neves and his cross was met by Trincao but the winger smashed the crossbar from inside the box.
Newcastle then immediately went up the other end and equalised, in controversial fashion. Saint-Maximin played a through ball for Joelinton but Sa was quick off his line to smother the chance at the forward’s feet. The goalkeeper took a knock in the process and stayed down injured, as Newcastle played on, allowing substitute Hendrick to rifle home from 25 yards.
Lage was furious that play was not stopped and was booked in the aftermath. However, Sa attempted to get up when he saw Hendrick had the ball and as a result VAR did not intervene. Had he stayed down, the goal may not have been given.
That goal was the last major action of the first half as the momentum Wolves’ had built during the half was sucked out of them after a sucker-punch of a goal. The hosts were not outstanding the first 45 minutes, but controlled the game and deserved to be in the lead.
As Wolves emerged for the second half, the atmosphere was flat among the crowd and the team mirrored that, with some laboured football.
Within five minutes, Sa was forced into a strong save to deny Saint-Maximin from close range. The chance came after Wolves fell asleep at a free-kick and allowed Newcastle to play it short down the wing and the resulting cross caused issues in the box.
Despite Wolves’ poor start to the half, they regained the lead after 58 minutes. It was a carbon copy of the first goal and once again created by Jimenez who rode a challenge in midfield and played a through ball for Hwang. The forward made a superb run and finished delightfully into the bottom corner.
From there, Wolves had spells of possession and looked after the ball well when they had it, but as the minutes ticked by they allowed Newcastle to grow into the game and start whipping balls into the box.
The pressure was relieved somewhat when Hwang went on a brilliant marauding run down the left flank and his cross just evaded Jimenez who came sliding in.
The Magpies kept pushing, however, as Wolves sat deeper in their defensive shape as the game entered the closing minutes. Some good aerial defending kept the visitors at bay as they continued putting crosses into the box.
In the end that resolute defending paid dividends as Wolves hung on for the result and entered the international break with back-to-back wins.
Wolves: Sa, Kilman, Coady, Saiss, Semedo, Neves, Moutinho, Marcal, Trincao (Dendoncker, 85), Hwang (Traore, 92), Jimenez.
Subs not used: Ruddy, Hoever, Ait-Nouri, Boly, Cundle, Podence, Silva.
Newcastle: Darlow, Manquillo (Murphy, 70), Fernandez, Clark, Ritchie, Hayden, Longstaff, Willock (Hendrick, 35), Almiron (Gayle, 77), Joelinton, Saint-Maximin.
Subs not sued: Gillespie, Schar, Lewis, Krafth, Fraser, Anderson.