The result left the Cherries, who have taken one point from their last seven league games, 19th on 27 points from 32 games, while Newcastle moved up to 13th on 42 points after stretching their unbeaten run to five games.
Allan Saint-Maximin shone with three assists as he gave his markers a torrid evening.
Dwight Gayle fired Newcastle ahead in the fifth minute after good work by Saint-Maximin and the irrepressible French forward picked the lock again in the 30th with some dazzling individual skill.
He weaved his way past Adam Smith and squared the ball back to Sean Longstaff, who buried a first-time shot into the roof of the net before limping off with a hamstring injury to make way for Miguel Almiron.
The Paraguayan made it 3-0 in the 57th minute with a superb shot from the edge of the penalty area, having burst through the middle of Bournemouth's porous defence after Saint-Maximin caused more damage on the left flank.
Saint-Maximin said the break forced by the COVID-19 pandemic had helped him get back to full fitness ahead of the home straight.
"The lockdown gave me a good opportunity to feel better and that is what has happened. I am happy because my team has won," the Frenchman told Sky Sports.
"It helped me a lot because I had time for recovery. It gave me that opportunity to play better so I want to keep going and keep working.
"Every game is like a final because we want to move up if possible. We played a great game today."
Bournemouth boss Eddie Howe conceded his team lacked confidence after losing 16 of their last 21 league games.
"The players are playing slightly tense, you could say understandably with the position they are in," he told the BBC.
"I urge them to play the game and not the situation but they are struggling a bit under the weight of that."