United dominated the opening 20 minutes, but failed to score on a frustrating afternoon for Louis van Gaal's team.
After a week in which they failed to land former target Pedro, United lacked a cutting edge up front.
Wayne Rooney's goal drought now stretches to 10 games
The captain thought he had put United ahead early on but his effort was ruled out for a marginal offside call.
The England captain had a shot blocked inside the area after the break, but otherwise failed to show he is the answer to United's scoring troubles.
It was not just Rooney who struggled in front of goal, however
Juan Mata and Memphis Depay also missed chances while Tim Krul performed some late heroics to deny substitute Javier Hernandez.
The result ended United's perfect start to the season and provided yet more evidence that Van Gaal needs to add more attacking players to his squad before the transfer window shuts in 10 days' time.
Rooney, who had scored 11 in 17 previous starts for United against Newcastle, looked to have ended his wait for a goal in the fourth minute when he latched on to Mata's through-ball and lifted the ball over Krul, but the goal was ruled out for offside
Despite his indifferent start to the season, Rooney's confidence was high
He drove a low shot at Krul from distance.
The Dutchman then pulled off a top save to deny Mata from a free-kick.
Steve McClaren, worried about his team's poor start, came down to the touchline from the directors box.
The Newcastle boss had every reason to be worried
His team were creaking under pressure from United's relentless attacking play
Mata and Rooney tested Krul again and Depay then rounded the Magpies' goalkeeper but was unable to finish.
As the first half progressed, Newcastle started coming back into the game.
Out of nowhere, Aleksandar Mitrovic leapt high to beat Matteo Darmian to the ball and rattle the bar.
Ayoze Perez then drilled a low shot wide after a mistake by Daley Blind.
United failed to take a grip of the game after the restart
Depay wasted a good chance by firing a free-kick into the wall.
Van Gaal brought Michael Carrick and Hernandez on for Bastian Schweinsteiger and Januzaj
Rooney dropped into the number 10 position, leaving Hernandez up front.
The Stretford End yelled "Attack! Attack! Attack!" Van Gaal's men obliged, but there was no breakthrough.
Steven Taylor blocked Rooney's volley in the box and Mata blazed way over the bar after being found by his captain with a deep cross.
Luke Shaw played a neat one-two with Morgan Schneiderlin before driving a low shot at Krul.
The Newcastle goalkeeper then pulled off the save of the match to deny Hernandez from eight yards.
Fabricio Coloccini blocked Antonio Valencia's shot, Chris Smalling struck the woodwork and a screamer from Carrick flew inches wide as United looked for another late goal at Old Trafford.
But it never came and Newcastle could have snatched all three points at the death had Papiss Cisse's cross been converted on the counter.
TWEET OF THE MATCH
Racing pundit and Newcastle fan John McCririck
@RealMcCririck "Krul + the Gang stirring defence
Toon @NUFC grabbing pt miraculous Best 0-0 draw of whole season? #HowayTheLads ! Brill Watch out Gunners!"
PLAYER RATINGS
Manchester United:
ROMERO: 6 out of 10
DARMIAN: 7
SMALLING: 8
BLIND: 6
SHAW: 7
SCHWEINSTEIGER: 6
SCHNEIDERLIN: 6
MATA: 6
JANUZAJ: 6
DEPAY: 6
ROONEY: 5
Substitutes:
CARRICK: 7
HERNANDEZ: 6
VALENCIA: 6
Newcastle:
KRUL: 8
MBEMBA: 6
TAYLOR: 7
COLOCCINI: 8
HAIDARA: 8
COLBACK: 7
ANITA: 6
PEREZ: 6
WIJNALDUM: 6
OBERTAN: 5
MITROVIC: 7
Substitutes:
THAUVIN: 6
TIOTE: 6
CISSE: 6
STAR PLAYER:
Fabricio Coloccini: Newcastle looked inept at the back against Swansea last week but today they were rigid and never lost concentration
Coloccini was the stand-out performer in the back four, throwing his body on the line when it mattered, particularly in the dying stages.
MOMENT OF THE MATCH
Tim Krul's save from Javier Hernandez
Krul was just as key to the result as Coloccini's efforts in front of him
The ball fell to Hernandez in the box in the 79th minute as United launched attack after attack but Krul came storming off his line and stretched his arms to deny the Mexican.
VIEW FROM THE BENCH
Steve McClaren resisted the temptation to give Florian Thauvin his full debut and instead chose to pack the midfield, with Aleksandar Mitrovic playing as a lone striker
The move paid off as Bastian Schweinsteiger and Morgan Schneiderlin had little impact on the game
Van Gaal bemoaned his team's failure to break down well-organised defensively-minded teams when they came to Old Trafford last year and he is yet to find a solution
Memphis Depay threatened occasionally but the hosts rarely looked like they were capable of scoring.
MOAN OF THE MATCH
Wayne Rooney: Failed once more in front of goal
Van Gaal insists Rooney is capable of leading the line for United, but he has now failed to score in 10 matches
Van Gaal's faith in the striker is admirable, but on this evidence the skipper is not up to the job.
WHO'S UP NEXT
Manchester United v Club Brugge (Champions League, Wednesday 26 August)
Newcastle v Northampton (Capital One Cup, Tuesday 25 August)
Source : PA
Source: PA