Finland had taken the lead at the Tampere Stadium on 15 minutes through Moshtagh Yaghoubi and England had to wait until midway through the second half to draw level.
Berahino, who scored the winner against Moldova last Thursday in Gareth Southgate's first game as coach, was again on target before Wisdom was shown the red card with 16 minutes to play.
Finland took the lead in avoidable circumstances, with Jack Butland rather embarrassingly caught out of position by a whipped, long-range free-kick by Yaghoubi in the 15th minute.
It was just reward for the hosts' early pressure, with the Stoke goalkeeper then tipping over a Robin Lod effort before James Ward-Prowse had England's first chance of note.
The Southampton man, making his second start for the Under 21s, again came close on the stroke of half-time, only to be denied by Fulham goalkeeper Jesse Joronen.
When play resumed, Butland was relieved to see Tim Vayrynen fire over after being beaten to the ball before substitute Harry Kane was denied moments after coming on.
England soon drew level, though, with fine work by Manchester United winger Wilfried Zaha allowing Berahino to finish from close range in the 67th minute.
Southgate's side pushed for a winner but fell just short as they played the final 16 minutes without skipper Wisdom, who was sent off following an altercation with Vayrynen.