Her award was the only one voted for by the public, and she was praised after her win by her Black Panther co-stars Andy Serkis and Danai Gurira.
They were presenting another award, but Serkis did a small victory dance.
Walking Dead star Gurira added: "Baby sis we love you, you are an inspiration always."
Here is Wright's speech in full:
"I identify myself as a child of God and I can't get up here without thanking God.
"A few years ago I saw myself in a deep state of depression and I literally wanted to quit acting.
"The only thing that pulled me out of it was God, my belief, my faith and my family, and an email from Bafta asking me to become part of the Bafta breakthrough Brits.
"I was like: "Let me try again'.
"So this wasn't an overnight thing, this wasn't a click of a finger success, and I'm still a work in progress, but I want to thank God, my family, my team…
"I want to thank everybody who said yes to me, that gave me a chance, and just saw my talent and saw what God placed in me, and said 'yes'.
"I want to encourage young people. You don't have to be young, you can be any age, but I want to encourage you - anyone going through a hard time... God made you and you're important, there might be some of you here who might be going through a hard time.
"I just want to encourage you and God loves you. Just let your light shine.
"And the category I'm in… this means so much to me, you guys all inspire me. All of you have inspired me so much, so God bless you, thank you, Jesus thank you, thank you."