United sprung from the traps swiftly, and Rashford’s curling attempt from the edge of the box required a strong left glove from Caoimhin Kelleher for Liverpool.
On minute nine, the Reds were only inches away from exploding into the lead.
Salah met a wonderful right-to-left pass from Darwin Nunez into the home penalty box with a powerful shot back across goal that narrowly missed the post.
And United scored the opening goal as the play reverted to its original course.
On the left side of the Liverpool area, Alejandro Garnacho was released into space. Although Kelleher blocked his shot, McTominay scored from a yard out on the rebound.
In the aftermath, Andy Robertson was right in the thick of things at both ends, stopping Garnacho at close range and then hooking a finish that was too high during a Reds counterattack.
As the duel went on, Dominik Szoboszlai cut a low shot into Andre Onana’s arms, and Kelleher pulled in a 25-yarder from Bruno Fernandes.
Soon after, both goalkeepers excelled in more difficult situations. McTominay attempted a side-footed shot from the center of the box, but Kelleher firmly blocked it, and Onana stopped Diaz at the near post.
In the 37th minute, Endo and Salah completed a one-two, and Endo rolled the ball into the left corner to give Klopp’s team a lead. However, following a VAR review, the offside flag was raised and the ruling was affirmed.
Nevertheless, before halftime, the Reds managed to tie the score and even take the lead.
Firstly, Jarell Quansah’s lunging attack from deep created a chance inside the box for Nunez to lay a calm assist back to Mac Allister, who, with Onana beaten, blasted a strike inside the right post.
Subsequently, during first-half added time, Nunez attempted a shot from the left side of the goal, but Onana parried it, setting up Salah for the goal. Old Trafford was stunned when the Egyptian smashed home the rebound from the woodwork.
The duel remained furious even as rain started to fall in Manchester.
Nunez quickly gained momentum down the right side and advanced to the byline, where his low cross nearly found its way into the net before Onana reflexively palmed the ball out.
When Fernandes burst into the left side of the Reds box, Quansah’s lunging recovery challenge sent a strike spinning off target, posing a threat.
After Salah passed Nunez in behind, Nunez prodded wide. Onana then deflected a low Szoboszlai effort and stopped Nunez’s thud on the angle.
While mostly keeping United at bay on the other end, Liverpool continued to hunt for what would have been a game-winning third goal.
But in the 87th minute, Antony turned on the ball inside the box and drilled a strike into the right corner to bring Erik ten Hag’s men level.
Rashford sidefooted wide when one on one with Kelleher, and Elliott had a sliced cross bounce against the post, giving either side a chance to win in normal time.
This extra-time match was anything but cagey, and United created a great opportunity when Garnacho’s pass off the heel down the left found Victor Lindelof, who made a run and struck the side netting with a smash.
But in minute 105, the Reds regained the upper hand.
Elliott gained possession thanks to some excellent work by Conor Bradley cutting in from the flank. Elliott’s long ball got a big deflection off Christian Eriksen and went into the left corner for a 3-2 score.
After Liverpool wasted the ball, Kelleher blocked a Harry Maguire attempt but was then overpowered by Rashford, who finished with a header after McTominay’s assist.
The same two then switched roles, allowing McTominay to play through in the middle of the box but miss with a prodded finish.
Amad started a counterattack for United as the game entered extra time, and he slid a low shot past Kelleher to send his team through.