Newcastle had a strong start to the first half and looked in control for the opening 15 minutes, coming closest to scoring in the 12th minute through Alexander Isak.
That shot was Newcastle's final shot of the first 45 minutes though, with Bournemouth quickly growing into the game and threatening to open the scoring on several occasions.
Debutant Evanilson was denied the ideal start to his Bournemouth career as Nick Pope expertly saved a left-footed strike, followed by Antoine Semenyo smashing an effort off the crossbar from outside the box 10 minutes later.
The Cherries gained further control following those two chances, beating the Magpies to every second ball and dominating the play, eventually breaking the deadlock when Marcus Tavernier was assisted after a brilliant piece of play from Semenyo.
Eddie Howe's men had a burst of action to start the second 45 minutes, but the game soon reverted to the pattern of the first half, with Bournemouth continuing to find more joy against their opponents.
A flurry of positive substitutions from Howe in the 58th and 70th minutes saw Newcastle step up their performance, threatening to equalise on several occasions but being denied by Neto and a stern Bournemouth defence.
Andoni Iraola's side were eventually undone after a period of mounting pressure as Harvey Barnes floated a cross towards the back post, allowing Anthony Gordon to tap into the net.
Dango Ouattara thought he had given the hosts a last-gasp winner when he headed in from a corner in the 93rd minute, but a swift VAR check broke Bournemouth hearts as the goal was ruled out, with the game eventually ending all square.
BOURNEMOUTH VS. NEWCASTLE UNITED HIGHLIGHTS
Semenyo denied by the crossbar vs. Newcastle United (27th min)
Semenyo receives the ball on the right flank and looks to cut inside onto his left foot, but Joelinton gets a toe to the ball, pushing the ball into a wider position.
Semenyo is able to keep a hold of possession and whips a left-footed strike towards the far corner, flying past Pope but smashing off the top of the crossbar.
Tavernier goal vs. Newcastle United (37th min, Bournemouth 1-0 Newcastle United)
Semenyo steals the ball away from Joelinton in the middle of the park and drives towards the Newcastle goal, bypassing two defenders before pulling the ball across the penalty area for Tavernier to sweep into the empty net.
Gordon goal vs. Bournemouth (76th min, Bournemouth 1-1 Newcastle United)
Barnes stands Julian Araujo up on the left wing before floating a teasing ball towards the back post, where Gordon is able to loose his marker and tap into the empty net to equalise for Newcastle.
Ouattara disallowed goal vs. Newcastle United (93rd min)
Ouattara rises highest to meet a fantastic delivery from a corner and heads the ball back across goal and into the net, giving Pope no chance of saving.
A swift VAR check for handball denied the goal as the ball was deemed to have come off of Ouattara's arm, breaking Bournemouth hearts.
MAN OF THE MATCH - ANTOINE SEMENYO
The forward had a particularly impressive second half, assisting the opening goal and coming close to scoring the opener after rattling the crossbar with a fierce long-range effort.
In a second half that saw Newcastle grow into the game and eventually equalise, Semenyo was a shining light for Bournemouth and continued driving the side forward at every opportunity, completing four dribbles throughout the game.
BOURNEMOUTH VS. NEWCASTLE UNITED MATCH STATS
Possession: Bournemouth 39%-61% Newcastle United
Shots: Bournemouth 16-14 Newcastle United
Shots on target: Bournemouth 4-5 Newcastle United
Corners: Bournemouth 8-9 Newcastle United
Fouls: Bournemouth 19-8 Newcastle United
WHAT NEXT?
Following Bournemouth's second 1-1 draw of the campaign, they will travel to face fellow Premier League side West Ham United in the EFL Cup during midweek, where Iraola will hope his side can pick up their first win of the season before they take on Everton at Goodison Park in the Premier League next weekend.
Newcastle also face Premier League opposition in their midweek EFL Cup fixture, travelling to Nottingham Forest for their second-round tie. The Magpies will then return to St James' Park for a challenging Premier League encounter with Tottenham Hotspur.