Eddie Howe's side held firm throughout the Premier League encounter against the Whites before taking the lead in the closing stages of the second-half, courtesy of Jonjo Shelvey's curling free-kick.
The Magpies were then able to see out the clash at Elland Road, despite suffering injuries to Joelinton, Paul Dummett and Jamaal Lascelles, to secure their first away win of the 2021/22 campaign.
Dúbravka, who produced a terrific reflex stop to deny Leeds' Dan James in the opening 45 minutes, is hopeful Newcastle can build on their much-needed win in their bid to secure their Premier League status next term.
"We really needed this win to lift our confidence," the Slovakian shot-stopper told nufc.co.uk. "I think I we deserved it because the work ethic we showed on the pitch today was great. We created some good chances and I'm happy that we scored a goal to win us the game.
"You need to have that little bit of luck sometimes but I think we deserved it because we worked so hard in the build-up to the game and then made it count. That is the most important thing. It's a massive three points.
"It is crucial that we stick together. We go game by game because this is the Premier League and you always have to be focussed on the next game.
"It's good that we have a few weeks off now because a few players picked up some injuries. Hopefully, they will have enough time to recover."
Following a 1-1 draw against Watford last week, conceding in the 88th minute, Dúbravka was pleased with the positive response from the squad after a late setback against the Hornets.
Backed by 2,650 away fans in West Yorkshire, Dúbravka also commended the raucous support of the Toon Army.
"I think, especially in the Watford game, we were there on the front foot," the 33-year-old recalled. "We were trying to manage it and the second-half was a little different. I don't know if we were afraid or scared because we were leading and it was disappointing not to win (against Watford).
"Today, we showed good attitude, which was great to see and this is how it should be.
"I'm very happy (with a clean sheet) but I have to say the guys played very well today. They defended well and you could see that togetherness on the pitch. We were everywhere and although Leeds created some chances, we were there.
"It was unbelievable support from the away fans. Hopefully, they enjoyed it too! They are supporting us every game and finally we have been able to give them something back which I'm very proud of."