A sensational long-range strike from Fabian Schär gave United the lead before Sean Longstaff doubled their advantage before half-time, with the youngster netting his first Premier League goal in front of a delighted Leazes End.
And the Slovakian goalkeeper made it back-to-back clean sheets as Burnley, unbeaten in their previous eight league matches, were unable to break down a spirited Newcastle backline in the second half.
Dúbravka - whose shut-out was his ninth this term - revealed his pleasure in his team mates' defensive efforts as Rafa Benítez's side moved seven points clear of the relegation zone.
"It was a tough game," Dubravka told nufc.co.uk. "We knew we were facing a quality team and that it would be very physical, especially with facing a lot of crosses, but we were ready for it.
"I think all of the players did very well and helped me a lot in blocking opponents when I went to catch the crosses. We will always support each other on the pitch and be together as a team, and this needs to be like this for every game.
"I was trying to help my team mates and do what the manager said, especially in dealing with balls into the box although I have to say that the players created a lot of space for myself and made it a lot easier in collecting some difficult balls. I'm happy that we got the win and a clean sheet is a bonus for us and for our confidence too so, hopefully, we can aim to get a good result in London (against West Ham) on Saturday."
Newcastle were unable to register a win in their opening five matches on Tyneside this season but Dúbravka believes United's current home form will be beneficial in their bid to secure Premier League status next season.
And, following the disappointment of conceding late goals against Tottenham and Wolves, the Slovakia international goalkeeper was pleased with the positive reaction from the squad to claim maximum points in their recent two matches, with the Magpies defeating Huddersfield by the same scoreline on Saturday.
Dúbravka added: "We were a little bit unlucky in the previous games and we thought we could have taken a lot more points and clean sheets. However, that's football as sometimes it's not always working or going in the right direction for you but I still think we have all been working really hard.
"We have ideas of what we should be doing on the pitch and are trying to do that in training and matches. We're always attempting to do what the gaffer says so it is important that the players have reacted well and it was great that we managed to score two goals.
"After a bad run at the start of the season, we have really needed these recent victories and clean sheets. It shows that it will not be easy for teams to come to St. James' Park and break us down, which is essential because it is important to pick up points at home."
