The Magpies fell behind in the closing stages of the first half following Matt Ritchie's unfortunate own goal before Callum Wilson equalised from the penalty spot as Joachim Andersen was shown a red card after the defender's last-man challenge on the United forward.
Steve Bruce's side were unable to break down the Cottagers, managed by former Newcastle midfielder Scott Parker, as they missed the chance to move into the top half of the Premier League.
Following a midweek loss at Leeds United, Newcastle made five changes to the side which suffered a 5-2 defeat at Elland Road, with Jonjo Shelvey, Matt Ritchie and Miguel Almirón all returning to the starting line-up while there were first starts of the season for defensive pair DeAndre Yedlin and Paul Dummett.
Former Newcastle striker Aleksandar Mitrović drew Karl Darlow into action after 10 seconds as the Serbian drilled an audacious effort from distance which was comfortably held by the United shot-stopper.
The hosts' opening goalscoring opportunity came through Wilson as Ritchie's inviting cross from the right wing found the forward inside the penalty area but his header towards goal flew straight down the throat of Fulham goalkeeper Alphonse Areola.
Darlow was on hand to deny Ademola Lookman from opening the scoring minutes later, as the United shot-stopper kept out the forward's free header following André-Frank Zambo Anguissa's dangerous cross from the left flank.
Bobby Decordova-Reid, a late addition to the Fulham starting line-up after Ivan Cavaleiro's injury in the warm-up, wasted a golden chance for the visitors after the half-hour mark, advancing behind the United defence following Mario Lemina's neat through ball but Fulham's top goalscorer this term failed to make full contact as the Jamaican's effort fired wide of the near post.
Almirón created arguably Newcastle's strongest chance of the first-half as Ritchie threaded a neat pass into the Paraguayan's path but his low drilled strike at goal was stopped by the diving Areola.
In the 42nd minute, Fulham took the lead through Ritchie's misfortune. As Tosin Adarabioyo headed towards goal after rising high from Tom Cairney's corner, Ritchie inadvertently turned the ball into his own net after striking the Scot's face.
In the second half, Newcastle got themselves back on level terms in the 64th minute as Wilson netted from the penalty spot to register his eighth league goal in 12 Premier League appearances.
After racing onto Almirón's through ball, the striker was brought down inside the box by Andersen and, following a lengthy VAR review, referee Graham Scott sent off the Danish centre-back.
Despite waiting several minutes to take his spot-kick, Wilson made no mistake from 12 yards after calmly sending his attempt down the middle of Areola's goal, recording his fourth successive penalty.
Darlow was forced into action shortly after United's equaliser, importantly beating away Lookman's fierce strike towards goal.
United, however, were unable to make their advantage pay with Wilson firing wide in the dying stages after controlling Ritchie's pass on the edge of the box before steering his effort wide of the target.
Newcastle United: Karl Darlow, DeAndre Yedlin, Federico Fernández (Isaac Hayden 45), Ciaran Clark, Paul Dummett (Ryan Fraser 78), Jonjo Shelvey (c), Sean Longstaff, Miguel Almirón, Matt Ritchie, Joelinton (Dwight Gayle 75), Callum Wilson.
Subs not used: Mark Gillespie, Emil Krafth, Jamal Lewis, Jeff Hendrick, Jacob Murphy, Andy Carroll.
