The match was a closely contested one, with both teams creating scoring opportunities, but neither could find the back of the net.
Bournemouth started the game strongly, putting pressure on Newcastle and creating the first real chance of the match through Tyler Adams, who forced a smart save from Nick Pope.
Newcastle had a few half-chances, including a shot from Jacob Murphy, but they struggled to create clear-cut opportunities.
The closest either side came to scoring was when Evanilson's cross was turned in by David Brooks, but the goal was ruled out for offside.
The second half was marked by strong appeals for a penalty from Nick Woltemade, who felt fouled by Bafodé Diakité, but the game remained goalless.
Both managers brought on substitutes in search of a breakthrough, but neither team could find a way past the other's defense.
Bournemouth pushed hard for a winner, but clear-cut opportunities were scarce, and the game ended in a 0-0 draw.
The result means Newcastle have now failed to score in four consecutive away Premier League games, extending their winless run to six games.
Bournemouth's three-match home winning streak in the Premier League came to an end, but they can take heart from a solid defensive display.