The result secured their second away win of the campaign and completed the double over the Clarets.
The match started at a frenetic pace, with Joelinton and Yoane Wissa both scoring inside the opening ten minutes to give Newcastle an early advantage. Bruno Guimaraes later added a late goal to seal the win, ensuring all three points returned to St James' Park.
Despite the comfortable scoreline, Newcastle's display was not convincing. However, Howe was more focused on the impressive mentality his players showed to ensure they come away with three crucial points.
"A massive win for us. I don't think it really matters tonight so much in terms of how we did it, we just needed to do it," said Howe.
"A really strong start from us, in recognition of how important the game was for us.
"I can't praise the players enough for how we battled through it. It was never going to be easy tonight. That second half was a massive 45 minutes for us.
"We needed to get over the line and put credit to the players for how they saw the game out and the character of the group."
The Magpies now face a busy schedule across the Premier League, FA Cup, Carabao Cup, and Champions League, making this win a timely confidence boost.