Sitting joint top with Wales coming into this clash, the Young Lions never looked like suffering their first ever defeat to the Finns, especially after Manchester United youngster Michael Keane had headed them into an early lead.
West Brom hitman Berahino then continued his fine form in front of goal by tapping in from close range to double the home side's lead.
That crucial second made the second-half little more than a mere procession, with Berahino's late third confirming Gareth Southgate's men are now three points clear at the top of their group, with plenty still to come in reserve.
With a wealth of attacking talent on show, Finland really struggled to handle the pace of the England side, and it seemed only a matter of time until the home side did break the deadlock.
The only surprise is that the goal came from a set-piece, as Keane firmly headed in Jame Ward-Prowse's inch-perfect free-kick to net him his second goal in as many games.
The goal did little to alter the tempo of the match, with the visitors constantly on the back foot.
And after an excellent save from a Luke Shaw cross-cum-shot by Fulham youngster Jesse Joronen in the Finland goal, Berahino was on hand to notch his fifth goal in his last four U21 appearances to put England in a comfortable position.
The Young Lions cruised after the interval, trying flicks and tricks without being pressured by the Finns.
Patrick O'Shaughnessy's dismissal made England's task even more comfortable, but chances came and went as they looked to extend their lead.
Substitute Tom Ince didn't quite connect when free at the back post, Wilfried Zaha saw his close-range effort well saved and Berahino was inches away from netting his second of the night, but saw his thunderous effort come back off the crossbar.
But the West Brom youngster didn't have to wait long to further add to his impressive goal tally in this campaign, neatly slotting the ball away after excellent work from substitute Jesse Lingard late on.
Jack Butland did have one late save to make but new boss Southgate will rarely get easier nights than this and will be very confident that his side can seal a trip to Czech Republic in two years' time.