The hosts won thanks to an own goal from defender Adam Smith, who unintentionally headed past Cherries [ Mark Travers after receiving a beautiful cross from Kieran Trippier.
Given that the home team generated the majority of the scoring opportunities, it was no more than Eddie Howe's team deserved.
The draw for the following game will take place on Thursday night.
The starting XI for the Magpies' matchup with Howe's former team featured goalkeeper Nick Pope, fullback Trippier, and forward Callum Wilson, who were all members of England's World Cup squad in Qatar.
Fabian Schar of Switzerland and Bruno Guimaraes of Brazil both started the game for the host team, who appeared to be nearly at full strength in their first competitive match since November 12.
In advance of