Joelinton, Yoane Wissa and Bruno Guimaraes scored in a rare away win that moved them to 10th in the league standings on 26 points, six out of the top four.
It is still not where supporters had envisioned the team at this point in the season after Newcastle won last year's League Cup, their first domestic trophy for 70 years, and reached the Champions League for the second time in three seasons.
"It was a massive win for us. We needed to win because we knew we were under pressure," Howe said. "I thought the lads responded really well, it was a really fast start. We scored some really good goals and then, us being us at this present time, we made it difficult for ourselves.
"The second half was nervy to a point. There were a couple of moments where Nick (Pope, Newcastle's goalkeeper) made massive saves for us. But overall I thought we showed real character and resilience to get over the line."
Newcastle's dip in form can partly be blamed on the departure of striker Alexander Isak to Liverpool in the close season.
The manager hoped Tuesday's win would lift the mood.
"I hope it relaxes us slightly - not in a negative way but in a positive way," Howe said.
"We want to play fluent, attacking football which is really good to watch. But you can only really do that when you are in a good mental place and relaxed. Hopefully that settles us down after a difficult period."