Ahead of the match, Man United's last piece of silverware had been the Europa League six years ago, but a two-goal success over the Magpies secured Erik ten Hag's first trophy since arriving as head coach last summer.
Newcastle were searching for their first piece of major silverware since 1955, but Eddie Howe's side found themselves two goals down at the interval, with Casemiro making the breakthrough before Marcus Rashford had a shot deflected past Loris Karius by Sven Botman.
Man United co-owner Avram Glazer was in attendance at Wembley amid the ongoing speculation surrounding the ownership of the club, who are still on for a quadruple this season due to their presence in the FA Cup and Europa League.
Rashford was named in the starting XI despite concerns over an injury that he picked up against Barcelona in the Europa League, while Diogo Dalot and Antony came into the side following Thursday's European counter with the La Liga leaders.
Newcastle's headline team news involved their goalkeeper, with Karius making his debut for the club and first competitive appearance in 728 days due to Nick Pope (suspended) and Martin Dubravka (ineligible) both being unavailable.
A lively start in the English capital saw both teams commit players forward in early attacks, with Rashford and Antony bright for Man United, while Allan Saint-Maximin and Miguel Almiron were involved for the magpies.
Dalot picked up the game's first yellow card for hacking Saint-Maximin to the ground in the ninth minute, leaving the Portugal international in a difficult situation with a lot of football left to play.
The first chance of the match came for Wout Weghorst in the 13th minute when he worked some space inside the Newcastle box, but the on-loan Man United striker could not find a route past Karius.
Another half-chance came for the Red Devils in the 15th minute when Dalot delivered a dangerous low cross into the Newcastle box, but Fabian Schar just about did enough to make the clearance, before Karius comfortably kept out an effort from Antony.
Man United goalkeeper David de Gea made a big save to keep out a low strike from Saint-Maximin in the 32nd minute after a low Sean Longstaff cross had caused problems inside the Red Devils penalty box.
Ten Hag's side took the lead in the 33rd minute of the contest, though, with Casemiro heading a Luke Shaw free kick into the back of the net.
There was a lengthy VAR check for a possible offside, but the goal stood, with the 20-time English champions making the breakthrough in the EFL Cup final.
Almiron scooped one over the crossbar in the 38th minute as the visitors looked to respond, but Man United scored their second less than one minute later.
Rashford proved his fitness in the build-up to kickoff, and the forward helped the Red Devils take a two-goal lead when he collected a pass from Weghorst before beating Karius, with a deflection off Botman making it difficult for the Newcastle goalkeeper.
The Magpies had an opportunity to halve the deficit in the 43rd minute when Dan Burn nodded an Almiron cross towards goal, but his effort was just wide of the post, before Karius did well to keep out a powerful Weghorst drive in the latter stages of the first period.
Man United had a chance to score a third early in the second half when Rashford found Fred just outside the Newcastle box, but the Brazilian placed the ball wide of the post, before Karius kept out a strike from Antony.
Aaron Wan-Bissaka was introduced for Dalot at the break, with the latter on a yellow card, and the Englishman made some important interceptions during a period of pressure from Newcastle.
Bruno Fernandes had a long-range strike deflected high of the crossbar, before Karius saved from Weghorst from the resulting corner, with Man United looking for a third, which would surely have ended the contest.
Newcastle were putting the pressure on down the other end, but Howe's side were struggling to carve out clear chances, with Man United defending their penalty box extremely well.
Saint-Maximin was a constant threat, but Wan-Bissaka was proving equal to the challenge, with the right-back impressively adapting to the pace of the match after entering at the break.
Joelinton had a powerful drive blocked away by Lisandro Martinez, with the Red Devils dropping deeper and deeper, which led to two substitutions being made.
Scott McTominay and Marcel Sabitzer both came off the Man United bench 20 minutes from time, with Fred and Weghorst leaving the field at Wembley, which saw Rashford go through the middle.
De Gea did well to make contact on a dangerous Trippier cross in the 72nd minute before Casemiro cleared inside a crowded box, but the offside flag was raised, before Karius denied Rashford down the other end.
The pressure from the Magpies, as expected, continued in the final stages, but Man United stood up to the challenge, with De Gea performing well under pressure; Wan-Bissaka had a chance to make it 3-0 four minutes from time, but his low effort was saved by Karius.
Jacob Murphy just missed the target with a brilliant low strike late on, before De Gea saved late from Joelinton, but it was not to be for Newcastle, who will now focus on their top-four challenge in the Premier League.
Man United, who had a big chance to score a third late on through Fernandes, have won the League Cup for the sixth time in their history, and they are also still active in the FA Cup and Europa League in what could be a very successful first season at the helm for Ten Hag.
Next up for the Red Devils is a home game against West Ham United in the fifth round of the FA Cup on Wednesday, while Newcastle will continue their Premier League game away to the champions Manchester City next weekend.