Charley Sanders scored twice to put the Pilgrims in control, but Dunkirk roared back into contention either side of half-time.
Macauley Diuk scored twice and Will Coutts struck a brilliant winner to send Dunkirk through.
United’s woes were compounded three minutes from time when midfielder James Reed was red-carded by referee Michael Shepherd after being adjudged to have committed a dangerous challenge.
Proceedings had started so well for the Pilgrims, with SANDERS rising to head the ball over Connor Touhig following Reed’s eighth minute free-kick.
United doubled their lead on the 20-minute mark with SANDERS slamming the ball home at the back post following Jordan Sowerby’s brilliant cross from the left.
Dunkirk’s pace on the break troubled United all night long and keeper Sam Vince had to make good saves to deny Jack Upton and Ryan Ejezie.
Ejezie, Coutts and Diuk terrorised the United rearguard and the visitors were rewarded with three goals inside a 12-minute spell either side of the break.
After Joel Earps had rattled the post following a short Josh Spencer backpass, DIUK made no mistake three minutes before half-time when he smashed home a near post drive which beat Vince with sheer brute force.
Dunkirk levelled five minutes after the break when DIUK raced through United’s offside trap to fire the ball low past an exposed Vince.
And the winning goal arrived on 54 minutes when COUTTS hammered home an angled drive, worthy of winning any game, following Diuk’s cross from the left.
United tried to respond but with striker Jordan Nuttell required to fill in at centre-half to tighten up United’s leaky backline, their attacking threat fell on the shoulders of Sanders and he was shackled by centre-halves Danny Brennan and Joe Brown.
Sanders did come close to a leveller following Reed’s corner, but a goalline clearance denied him, while Aaron Eyett was also denied by a terrific close-range block moments later.
As it was, Dunkirk came closest to adding to the scoreline with man-of-the-match Diuk seeing his drive deflect a fraction too high to deny him a hat-trick.
Drama was still to unfold on 87 minutes when referee Shepherd consulted with both assistants before opting to dismiss Reed for a high challenge.
Boston (4-4-2): Sam Vince; Niall Delahoy, Josh Spencer (Leon Squire 54), Todd Devlin, Charlie Rossington; Aaron Eyett, James Reed, Keiron Elliott, Jordan Sowerby (Joe Briers 46); Jordan Nuttell, Charley Sanders. Subs (not used): Curtis Revell, Charlie Melville, Jack Hall.
Referee: Michael Shepherd