The Arsenal winger struck England's equaliser and also struck in the penalty shootout.
Saka, who missed in England's Euro 2020 final shootout defeat by Italy, kept his cool to convert.
"He is so brave, he's one of our best so we were never in any question that he was going to take one," coach Gareth Southgate said of the midfielder.
Saka said: "To come back from something like that was really difficult. I used that to make me stronger. Today I took the chance and I'm happy.
"Hopefully next game we can win in the 90 minutes but if this is what it takes, we'll do anything."
Trent Alexander-Arnold scored the winning spotkick.
"Incredible," said Alexander-Arnold. "These are the goals and aims that we set for ourselves. The team showed a lot of character, belief, a lot of heart and spirit out there. We dug deep when it mattered most.
"A lot of practice goes into that moment," he added of the penalty he smashed into the top corner. "I practice. I knew what spot. I knew I just needed to execute it and I went out and did that."
Southgate also said: "Huge performance, huge result for us.
"We had to be tactically spot on. To come from behind again and show the character and resilience that we did... winning tournaments isn't just about playing well. I thought we did play well today but you've also got to show all those other attributes to win and we showed them all tonight."