The Pilgrims had to survive for 40 minutes after Bradley Thomas was controversially sent off following a clash with Martin Gritton.
But Boston belied their lowly position to claim their first away win since mid December, thanks to an amazing injury time let-off when Mansfield wingman Matt Hamshaw blazed over an empty net from an acute angle.
The visitors - unable to play new signings Michael Proctor and John McCombe - created the better chances of a poor opening. David Farrell's cross just eluding Drewe Broughton, and Stewart Talbot's crashing shot deflecting wide off Alex John-Baptiste.
In the 10th minute Bradley Thomas' close range pile-driver was beaten away by the alert Jason White with a fine reflex save as the Pilgrims continued to dominate.
The sluggish Stags struggled to get into the game, although Bryan Hodge's low 20 yard free-kick almost found three players rushing in at the far post. Then the midfielder's deeper set piece was glanced straight to the keeper by Gritton.
But Boston eventually found the breakthrough their adventurous start deserved in the 18th minute. The unmarked Talbot rifling a low 16-yard drive into the bottom corner after Mansfield failed to clear a Jamie Clarke throw.
On the half-hour the Stags levelled after their first real spell of pressure, courtesy of a fine overlap and cross by full back Gareth Jelleyman, which was headed in off the underside of the bar by Barry Conlon.
Boston came bouncing back to restore their lead five minutes before half-time, Francis Green breaking down the left and crossing for Broughton to head powerfully in from six yards.
Three minutes into the second half Boston keeper Andy Marriott three times denied the home side an equaliser - clinging onto John-Baptiste's fierce drive on a breakaway, blocking Stephen Dawson's penetrating low cross, and cutting out another fine cross from Hamshaw as Simon Brown waited to pounce.
But then Boston's hopes of a vital victory were made even harder when Thomas was sent off following a clash with Gritton in the 54th minute. However, Mansfield failed to make their man advantage count.
Teenager Danny Sleath made his debut for the Stags as a 74th-minute substitute, and was later denied by keeper Marriott diving full length to tip his 25-yard drive around the post.