Casemiro headed home Luke Shaw's pinpoint delivery to opening the scoring at Wembley before Rashford's deflected shot found its way past Loris Karius to double his side's advantage.
The Magpies fought valiantly and went close, most notably through Allan Saint-Maximin and Jacob Murphy, but Eddie Howe's men couldn't find a way back into the game as their memorable winning run in this season's competition came to an end at the final hurdle.
Newcastle, backed by a boisterous, magnificent following in their half of Wembley, started confidently, with Saint-Maximin looking particularly threatening. The Red Devils, though, were first to register a shot on target, though Wout Weghorst's scuffed effort posed no problems for goalkeeper Karius.
Karius, in for his competitive bow in place of the suspended Nick Pope, was marginally the busier of the stoppers early on, catching Antony's curling strike with ease. A trademark Fabian Schär run from deep resulted in the Swiss centre back meeting a Kieran Trippier cross at the other end, but he couldn't keep his header down as he collided with Lisandro Martinez.
Just after the half hour, the Magpies were denied after carving out their best chance of the opening half. Sean Longstaff's low ball across the box was picked up by Saint-Maximin and his terrific skill took him past Diogo Dalot, but David De Gea did well to throw an instictive arm at the ball to repel it.
A few minutes later, they fell behind. Casemiro applied the final touch, glancing home past Karius, but it owed much to a fine cross from Shaw from the left. The goal was given after a VAR review and, six minutes before the break, Erik ten Hag's men struck again.
This time, it was Rashford who found the target. The in-form forward timed his run as he overlapped Weghorst and when the big Dutchman played him in, he took aim, with the shot taking a deflection off Sven Botman and looping in beyond Karius.
The dangerous Weghorst forced an excellent save from United's German keeper in stoppage time and Howe responded by replacing Longstaff with Alexander Isak at the break. But it was ten Hag's side who started the second period on the front foot, with Fred pulling a decent chance wide of the target just moments after the restart.
It took a while for Newcastle to settle back into the contest but after the hour, they began to turn the screw, led by Saint-Maximin. A long ball into the box had De Gea scrambling before Joelinton fired goalwards, but Martinez threw himself in the way of the Brazilian's drive.
A low Rashford attempt drew a good save from Karius with just over quarter of an hour left and substitute Marcel Sabitzer blazed over after that chance, however, with the game beginning to slip away from the Magpies.
Substitute Murphy's endeavour almost brought a consolation as he whipped one over the top and whistled one just wide from distance, but it wasn't to be Newcastle's evening as they left the famous old stadium empty-handed.
