The West Brom forward netted for the second successive game as Gareth Southgate's side were reduced to 10 men after the Liverpool defender's dismissal in the 74th minute
The 20-year-old West Brom forward followed up on his winning goal against Moldova last Thursday with the equaliser which maintains England's unbeaten start to European Under-21 Championship Group 1.
Southgate's side were forced to play the final 16 minutes with 10 men after Liverpool defender Andre Wisdom was sent off for kicking out at Tim Vayrynen.
Moshtagh Yaghoubi's free kick from 30 yards out opened the scoring for the hosts after he whipped in an effort from the left which caught Jack Butland by surprise as the Stoke City goalkeeper was anticipating a cross, rather than a shot.
England had a strong case for a penalty before the close of the first half after Berahino was caught by Finland goalkeeper Jesse Joronen inside the box, while James Ward-Prowse had two chances to put the visitors level.
Second-half substitute Harry Kane had another opportunity to pull Southgate's men level however Joronen was equal to the Tottenham forward's strike after he was put through on goal.
But England's continued pressure was rewarded after 67 minutes as Wilfried Zaha's cross from the right wing was met by Berahino, who finished neatly from close range.
Wisdom's dismissal threatened to set up a nervy finish for England but the visitors could have escaped with a second successive Group 1 victory had Joronen not denied Eric Dier from two set pieces.