Another Ward-Prowse delivery nearly resulted in a second goal for England but John Stones saw his header deflect wide.
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England continued to control the game and in the 37th minute the hosts were able to double their lead.
At the start of the second half, Jesse Joronen was forced into a save from Shaw's powerful drive.
The keeper was called into action soon after when he pushed behind a strike from Ward-Prowse.
Finland's task was made even harder when Patrick O'Shaughnessy saw red for a foul on Shaw.
England came close to adding a third goal through Wilfried Zaha, who cut in from the left wing and curled a shot against the crossbar.
The hosts sealed their victory in the final minute when Berahino was played through on goal and slid the ball past the keeper.
Tonight's result means that England stay top of their qualifying group with 13 points from their first five matches.