It was an eventful second match in charge for new Young Lions boss Gareth Southgate, whose first game at the helm ended in a 1-0 win over minnows Moldova last week.
Berahino netted that night and was on the scoresheet again in Tampere, grabbing a second-half equaliser in a European Championship qualifier that did not go to plan.
Finland took the lead in avoidable circumstances, with Butland rather embarrassingly caught out of position by a whipped, long-range free-kick by Moshtagh Yaghoubi in the 15th minute.
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's 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.