The League One outfit take the lead following an uncharacteristic error by David Wheater, who poked the ball past goalkeeper Danny Coyne after 27 minutes, following a cross from the right by Chris Hackett.
The Championship side then huffed and puffed for the reminder of the match and rarely looked like equalising until 12 minutes from time when a speculative Rhys Williams shot from 25 yards whistled past Lions' goalkeeper David Forde.
BORO: Danny Coyne, Justin Hoyte (Tony McMahon, 61), Robert Huth , David Wheater , Jonathan Ground , Mark Yeates, Julio Arca (Gary O'Neill 46) , Didier Digard ( Rhys Williams, 61), Adam Johnson , Jeremie Aliadiere , Marvin Emnes (Jon Franks, 81)
Subs not used: Adan Smith, Seb Hines , Andrew Taylor, Josh Walker, Nathan Porritt Goals: Wheater OG 27mins, Williams 78m.
Att:3,620