Stevenage took the lead in the 43rd minute of Tuesday night’s League One clash at Dean Court when Craig Reid beat the offside trap to convert a low right-footed shot.
Cherries manager Lee Bradbury sent on Harry Arter at the start of the second half in place of Steven Gregory and the move paid off within two minutes. Marc Pugh crossed from the left and Arter was unmarked to turn the ball home.
The turning point of the match came in the 64th minute when Barrett handled a goalbound shot from Stacy Long on the line and was shown a red card.
John Mousinho stepped up to score the subsequent penalty, sending goalkeeper Darryl Flahavan the wrong way.
Stevenage goalkeeper Chris Day made an outstanding save to deny Arter a second equaliser in the 71st minute before the visitors made sure of their first victory in the first minute of injury time when striker Byron Harrison scored from 10 yards after Scott Laird had got down the left.