The Pilgrims took an early lead against AFC Rushden and Diamonds at The Jakemans Stadium through Holland but found themselves 3-1 down at half-time.
Gaukroger's excellent free-kick reduced the arrears to 3-2 and Bark was on target once Rushden had scored their fourth goal.
Boston (3-5-2): Seth Greeves; Jamie Gaukroger, Harry Cranfield, Nathan Stevens (Daniel Fisher 60); Xander Crashley (Dylan Mercer 55), Taylor Gray (Cole Willerton 70), Marshall Young, Lewis Bontoft, Will Jackson; Jenson Bark, Harrison Holland (Dougie Barrett 50). Sub (not used): Marc Tucker.