MANCHESTER, England -- So, it turns out Erik ten Hag can motivate and lead his Manchester United team to victory against a formidable opponent.

Man United's 4-3 win in the FA Cup quarterfinal against Liverpool on Sunday answered so many questions about the manager's ability to make it count when it matters on a day when Old Trafford felt like the impregnable fortress of the Sir Alex Ferguson era.

In a thrilling game that had absolutely everything, substitute Amad Diallo's winning goal in stoppage time at the end of extra time sealed an FA Cup semifinal against EFL Championship side Coventry City next month. Amad, whose season has been blighted by injury, was sent off for a second yellow card after removing his shirt in celebration in perhaps the most unsympathetic dismissal of the year.

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With Ten Hag's future as United manager still anything but secure, there is no lack of irony in the fact that Coventry are managed by Mark Robins -- the man often credited with keeping Alex Ferguson in a job with a crucial game-winning goal for United in an FA Cup tie against Nottingham Forest in 1990. Could Robins once again hold the fate of a United manager in his hands? Ten Hag will certainly hope not.

We already know that manager Jurgen Klopp will be leaving Liverpool at the end of the season, and this defeat means he will not be celebrating a quadruple when he heads through the Anfield exit door.

That is down to Ten Hag finding a way to turn a losing situation into a winning one with bold substitutions as United chased the game. Then Ten Hag threw caution to the wind by playing out the final minutes of extra-time with Harry Maguire, Diogo Dalot and Bruno Fernandes forming a makeshift back three.

"United took a lot of risks -- I absolutely respect that," Klopp said.

How much of that was by accident or design is up for debate, but Ten Hag at least influenced the outcome of the game. His first change, replacing Rasmus Hojlund with Antony, paid dividends when the Brazil winger made it 2-2 late in regulation time with only his second goal of the season.

By that stage, Ten Had had also introduced Christian Eriksen and Amad for Kobbie Mainoo and Raphaël Varane -- two attacking players in favour more defensive ones. Even though they felt like desperate measures for desperate times, his decisions paid off.

Having taken a 10th-minute lead through Scott McTominay, United had seen their advantage overturned as Liverpool went in 2-1 ahead at half-time following goals from Alexis Mac Allister and Mohamed Salah just before the intermission.

At that point, an air of resignation descended over Old Trafford. United have lost five times in this season after scoring first -- only Brentford (7) have suffered more defeats when leading -- and United were trailing against one of the best teams in the world.

It seemed more likely that the day would get worse rather than better for United, but having been questioned all season over an apparent lack of unity and fighting spirit, Ten Hag's players summoned every last drop of those qualities.

"The first 30 minutes was the best of our whole season," Ten Hag said. "We were acting as a team, but then we got gaps between the lines, and you can't allow this against one of the best teams in Europe.

"They outplayed us. Then we made changes, we took risks and the players were wonderful. The attitude was great, a strong belief to win this game."

United rode their luck with Liverpool dominating and missing chances, but Antony's 87th-minute equaliser energised United. A win without the need of extra time was only denied due to a remarkable miss by Marcus Rashford, when he shot wide from six yards with the last kick of regulation.

When Harvey Elliott made it 3-2 to restore Liverpool's lead in the 105th minute, United looked drained of energy and belief, but in the brief huddle during the extra-time break, Ten Hag rallied his players for one last push. And he went for broke again, this time replacing defender Victor Lindelöf with attacking midfielder Mason Mount.

For so long, United's supporters have urged Ten Hag to be bolder, to take more risks, and here he was, answering that call with time running out against the club's biggest rivals.

The game had now become like a basketball match -- end to end, gaps everywhere and chances for both teams to score. And Rashford, whose lack of goals has contributed to the problems experienced by Ten Hag, made up for his earlier miss by equalising on 112 minutes with a low strike beyond goalkeeper Caoimhin Kelleher.

Old Trafford erupted again, but just as this classic tie looked set for a penalty shoot-out, Amad made it 4-3 after charging down a free-kick on the edge of the United penalty area. He raced clear with Alejandro Garnacho and, after an eighty-yard sprint, scored with a shot in the far corner.

Ferguson, who retired as manager in 2013, celebrated wildly in the directors' box, just like every other United fan in the ground. This stadium has not seen an occasion like this since Ferguson's time as manager and, less than a month after new minority owner Jim Ratcliffe talked of "knocking Manchester City and Liverpool off their perch," Ten Hag had overseen a win that derailed Liverpool's hopes of a quadruple.

It was a signature win for Ten Hag, but for United to truly to be back and for Ten Hag to survive in his job, the club has to enjoy their own success rather than merely stopping their rivals securing it.

This win showed what the future can hold, and it certainly doesn't hurt Ten Hag's chances of surviving at Old Trafford despite calls for his sacking. But United's next challenge is to win a Premier League game at Brentford. Being able to do that, away from the emotion of beating Liverpool, is what will really dictate the manager's future.

"We are still fighting," Ten Hag said. "For a long time in the season, we are far behind that level, but we are putting pressure on Spurs and Villa. Every game is a final, and we lost one final against Fulham. Our goal is the Champions League and silverware."

Ten Hag might need to deliver both to have any chance of keeping his job, but this win keeps him alive and kicking.