A Steven Taylor own goal gave the Cherries a first-half lead, before Joshua King then struck to make it 2-0 after 70 minutes.
But Newcastle fought back through Ayoze Perez before Charlie Daniels then fired in from range to secure the victory.
"It's a big win," explained Howe.
"I thought it was thoroughly deserved because we were very good for the majority of the game.
"We made it a little bit nervy towards the end, but the third goal was the icing on the top of the cake.
"It has capped off a brilliant week for us - seven points."
Having netted three goals away from home, the Cherries boss was also quick to praise his attacking force.
"I thought we had a real threat about us today," Howe continued.
"Benik Afobe, Max Gradel, Joshua King, Matt Ritchie, they were all very lively and gave Newcastle problems.
"It's great to see us score three goals away from home and look so threatening. Now we must carry that into our next game."
Cherries Player HD subscribers can see all the post Newcastle reaction here