The result, which maintains England’s unbeaten start to the campaign and keeps them on top of Group One, was achieved thanks to a Michael Keane header and a brace from Berahino.
The West Brom striker, who now has six goals in four outings for the Young Lions and was named as man-of-the-match, hailed his "brilliant" team-mates after the game.
He said: “The spirit is brilliant and the lads have been brilliant. They all want to qualify and they’re all putting their all in.
"And we’ve just got to take the performance into the San Marino match and do the job there as well.
Video highlights of the Euro qualifier in Milton Keynes.
“I could’ve had more, I'm a bit disappointed to hit the crossbar as I was looking for the hat-trick! But I thank God for the two goals and another good team performance.
“It helps a lot because we’re at home. And the fans have been brilliant – I couldn’t thank them enough for today. Hopefully we will get the three points against San Marino [on Tuesday].”
The young forward also revealed a message on his vest after scoring the first goal, a celebration which saw him cautioned, and said he was keen to pay tribute to his late father.
He explained: "I just had a few problems at home and I’d been thinking about my dad. And today I wanted to score a lot for my dad. My mum’s watching at home and I wanted to show her I still love my dad and miss him.”
