Ben Mee's own goal with just three minutes and 35 seconds on the clock was the fastest away goal Newcastle have scored since Yohan Cabaye netted after just two minutes against Sunderland in the Tyne-Wear derby back in October 2012.
The Magpies made a terrible start to the season but can now look up, although Benitez will ensure his side keep their feet on the ground.
Sky Sports commentator Andy Hinchcliffe said: "How on earth has that gone past the post?"
"Winning is massive because it gives us more confidence". I think we did well, and hopefully we can carry on. The players did it and were incredible in terms of effort, organisation and team spirit.
Newcastle surely could not believe their luck, and the goal allowed them to stick to their compact shape and invite Burnley to try to play through them.
"The team was pushing quite hard, we started well".
The Magpies took a fourth-minute lead after a Federico Fernandez shot from 20 metres took a heavy deflection off Mee and Clark then made it 2-0 with a superb header in the 23rd minute as he met a fine cross from the left by Matt Ritchie.
He said: "A lot of the aspects of the game I was very pleased with".
The pantheon of diabolical Premier League misses has a new entry with Ritchie's incredible effort. Obviously the frustration is you don't get a result.
Ritchie looked set to make sure of the points early in the second half but the winger, who had set up Clark's goal, bizarrely slotted wide at the back post after DeAndre Yedlin beat Charlie Taylor for pace.
The whistle came at the right time for Newcastle and the start of the second half again saw the away side possessing the greater impetus. "We've had to fight for everything we've got so far and we'll continue to do that".