New signing Francis Green scored twice in the opening 12 minutes of his debut against his former club, but Danny Sleath and Tom Ward restored parity at half-time.
Marc Newsham and Jason Lee completed the turnaround with strikes inside the space of two second half minutes.
United were full value for their victory, despite trailing by two Green goals with less than a quarter-of-an-hour on the clock.
Eastwood had taken the lead after just 120 seconds. Steven Istead whipped a ball in from the Town right and GREEN held off the challenge of former team-mate Lee Canoville to drill a low effort across Paul Bastock and into the far corner.
United responded and had five clear-cut chances before Green’s second strike 10 minutes later. James Severn made a brilliant save to keep out Ben Milnes’ header, while Ward had a header hacked off the line by Cameron Fearon and Tyrone Kirk’s shot was beaten away by Severn.
Newsham also headed over the top from a Kirk cross, before putting the ball in the net from an offside position, but Eastwood were soon two goals to the good.
Seizing possession 25 yards from goal, GREEN let fly with a dipping volley which gave Bastock absolutely no chance.
United cranked up the pressure once more and Lee’s angled drive was beaten to safety by Severn, although their breakthrough finally arrived after 19 minutes, with SLEATH drilling the ball low into the net from 20 yards.
Green’s one-man crusade continued with another vicious long-range strike which Bastock did well to tip over the crossbar.
United levelled seven minutes before half-time. Milnes delivered an inviting corner and WARD got in between the Eastwood keeper and defence to bury a close-range header.
Boston were in determined form after the break too. Ian Ross’ deep cross was headed against the outside of the post by Lee, but United were soon in front for the first time.
Lee flicked the ball into the path of NEWSHAM, who held off the challenge of Fearon to drive the ball underneath Severn at the near post.
United went further in front on the hour mark. Milnes’ first shot was blocked and LEE swivelled to lash home the loose ball high to Severn’s left.
Leon Constantine was soon introduced for his United debut, but the Pilgrims slowly lost the rhythm that had been built up and Eastwood created the two best chances during the closing stages.
Substitute Danny Elliott rattled the post with an angled cross-shot and Bastock denied Green his hat-trick with a terrific diving save.
Boston (4-3-3): Paul Bastock; Jordan Fairclough, Lee Canoville, Tom Ward, Kevin Austin; Ben Milnes (Chris Hall 71), Ian Ross, Danny Sleath; Tyrone Kirk (Ryan Semple 61), Jason Lee (Leon Constantine 63), Marc Newsham. Subs (not used): Ben Fairclough, Jason Field.
Eastwood (4-5-1): James Severn; Cameron Fearon (Alex Troke 89), David Haggerty, Kallum Keane, Sam Benjamin; Steven Istead, Josh Burge, Mitchell Hanson, Ross Gardner (Danny Elliott 76), Markell Bailey (Jevaise Christie 61); Francis Green. Subs (not used): Jason Bradley, Richard Cooper.
Referee: Neil Hair