Rafa Benítez’s men were looking for a third straight Premier League win on their second-ever visit to the London Stadium, with United fielding the same team that beat Burnley 2-0 in midweek.
But Rice’s early header and Noble’s penalty saw them head into the break with a two-goal deficit to overturn.
And, while they pushed hard to find a way through in the second period, the Hammers held out to keep a clean sheet and take all three points in the capital.
United found themselves behind barely six minutes into the contest. Robert Snodgrass’ inswinging corner found Rice five yards from goal, and he rose to nod in the opener.
It wasn’t the start Benítez had hoped for, and his side struggled to prise open the Hammers’ backline. They showed plenty of industry, typically, despite Ayoze Pérez’s belated finish being ruled out for offside and though Salomón Rondón was well marshalled by Issa Diop and Angelo Ogbonna in the first 45 minutes, he did see a back post header drift wide of the target.
With five minutes of the half remaining, it was two. Javier Hernandez found space in the box and drew a challenge from Florian Lejeune, who clipped the Mexican forward. Referee Chris Kavanagh pointed to the spot, and the hosts’ skipper Noble dispatched the penalty high into the top left-hand corner beyond Martin Dúbravka.
Fabian Schär almost had a chance to get one back in added time as he turned onto a loose ball in the box, but Diop denied him with a perfectly-timed tackle, whipping the ball off the Magpies man’s foot just as he looked to shoot.
Benítez replaced Sean Longstaff with Mo Diamé at the break and the visitors looked to attack from the off, with Isaac Hayden curling a low shot past the upright and Pérez dragging another one wide after collecting Rondón’s through ball.
The on-loan Venezuelan frontman then tested Lukasz Fabianski with a low effort from a tight angle before the Hammers’ Hernandez fired a pair of warnings, stabbing over a cross before finding the sidenetting.
The final quarter of the game saw United revert to a back four, with Paul Dummett on in place of Schär. Rondón saw a back-post header blocked and Miguel Almirón pulled a shot wide inside the last 20 minutes, before United’s number nine went even closer, striking the base of the post with a well-struck free kick.
But a goal wasn’t forthcoming for Newcastle, who must now look for a fourth successive home victory when Everton arrive at St. James’ Park next Saturday afternoon.
