The Pilgrims recovered from the setback of falling behind to Vamara Sanogo on 19 minutes and won it courtesy of brilliant long-range strikes from Kaine Felix six minutes before half-time and Jay Rollins four minutes afterwards.
The result left Boro needing to win both remaining matches to finish above the Pilgrims, who can clinch a top five berth with victory at Stalybridge Celtic on Saturday.
United boss Dennis Greene had opted to name an unchanged line-up, with defender Joe Burgess fit enough for inclusion on the bench.
An early Sanogo drive was turned wide by Fabian Spiess following a rare slip from Carl Piergianni, while Zak Mills was forced to head away in his own goalmouth after Rob Duffy had nodded Kristian Scott's corner goalwards.
Nuneaton were rewarded for their bright start when SANOGO rose highest to power home Scott's deep free-kick beyond the reach of Spiess.
There was almost an immediate response for the Pilgrims, but Garner's header bounced down off the underside of the bar and to safety.
Mills subsequently produced a stupendous block to divert Elliott Whitehouse's drive and divert the ball behind for a corner.
It laid the platform for United's comeback and once Piergianni's bullet header had flown wide following Lewis Hilliard's corner, the Pilgrims levelled on 39 minutes.
Hilliard's eighth corner of the game was cleared as far as FELIX who spectacularly blasted the ball home into the top corner from 25 yards to restore parity.
United flew out of the blocks after the break and Hilliard's rising drive was almost fumbled above his head by Smith but the keeper recovered to save.
The Pilgrims went in front on 49 minutes when ROLLINS rattled home a beauty from 20 yards into the top corner and beyond Smith's reach following Dayle Southwell's neat assist.
Southwell's stinging free-kick and Rollins' firm drive brought further saves out of Smith and although Nuneaton applied plenty of late pressure, the closest they came to equalising was when Joe Maguire's close-range shot was scrambled behind for a corner.
Boston (4-3-3): Fabian Spiess; Zak Mills, Nat Brown, Carl Piergianni, Dylan McEvoy; Scott Garner, Grant Roberts, Lewis Hilliard; Kaine Felix, Dayle Southwell (Joe Burgess 85), Jay Rollins (Mark Jones 78). Subs (not used): Conner Robinson, Cameron Johnson, Malachi Lavelle-Moore.
Nuneaton (4-1-2-1-2): Jordan Smith; Sam Warburton, Joe Maguire, Lathaniel Rowe-Turner, Cieron Keane (James Reid 87); David Morgan; Shane Byrne, Kristian Scott; Elliott Whitehouse; Rob Duffy (Joe Ironside 68), Vamara Sanogo (Tyrell Waite 88). Subs (not used): Jack Lane, Zeus De La Paz (gk).
Referee: Lloyd Wood.
Attendance: 2,037 (170 visitors).