The Magpies, targeting a first league victory against the Cherries since a 4-1 triumph in July 2020, were unable to muster a number of clear-cut goalscoring opportunities at the Vitality Stadium, with Jacob Murphy going close for the visitors in the first-half with their sole shot on target during the 90 minutes.
Eddie Howe's men, though, were resolute in defence and restricted the hosts, seeking a fourth league win in a row, to a mere two shots on target as they recorded a third successive clean sheet on the road.
Seven changes were made from Thursday's UEFA Champions League defeat against FC Barcelona at St. James' Park, with Malick Thiaw handed his full United debut since arriving from Serie A side AC Milan last month while Lewis Hall was awarded his first Premier League start since February following a foot injury.
Nick Pope was forced into early action as the 33-year-old goalkeeper blocked Tyler Adams' fierce first-time strike from the edge of the penalty area, getting an important foot to the ball.
Murphy, who scored eight Premier League goals last season, went close to opening his goalscoring account for the current campaign after his drilled effort from a tight angle, following neat link-up play involving Nick Woltemade and Sandro Tonali, was blocked by Bournemouth goalkeeper Djordje Petrović.
Newcastle were fortunate to remain on level terms as David Brooks tapped the ball into the net from Evanilson's pass towards the back post but the goal was disallowed after, following a VAR check, the Cherries captain had strayed into an offside position.
Sandro Tonali was unable to fire the visitors into the lead before the half-hour mark as the Italian midfielder controlled Lewis Miley's pass on the edge of the box before directing his lofted attempt over the crossbar.
In the second-half, Newcastle were appealing for a penalty as Woltemade looked to have been brought down by Bafodé Diakité, with the Cherries centre-back pulling the German striker's shirt, but referee Rob Jones deemed insufficient contact inside the box.
Harvey Barnes, introduced from the substitutes' bench, was unable to make a goalscoring impact as the Burnley-born winger, one goal shy of a half-century of Premier League strikes, completed a mazy run into the box before Bournemouth defender James Hill completed a last-ditch challenge to prevent the Magpies forward from firing a shot towards goal.
There was a welcomed return for Jamaal Lascelles as the 31-year-old centre-back made his first Premier League appearance since February 2024, after sustaining an anterior cruciate ligament injury, in the closing stages.
With the full-time whistle nearing, Pope produced a crucial stoppage-time save to ensure a third successive shutout in the English top-flight, turning away Justin Kluivert's powerful free-kick out for a corner.
Newcastle United: Nick Pope, Lewis Hall, Sven Botman, Sandro Tonali, Malick Thiaw (Jamaal Lascelles 84), Tino Livramento, Jacob Murphy (Harvey Barnes 62), Nick Woltemade (Will Osula 84), Joe Willock (Anthony Elanga 62), Dan Burn (c), Lewis Miley.
Subs not used: Aaron Ramsdale, Kieran Trippier, Joelinton, Emil Krafth, Bruno Guimarães.