Maguire struck in the 26th minute, following a brilliant Jacob Hazel assist, to hand United all three points at the Jakemans Community Stadium.
The result lifted the Pilgrims five points clear of the bottom four - with four matches to play.
United were unchanged from their midweek success over Aldershot Town but it was the visitors who made the brighter start.
Matty Kosylo robbed possession in a dangerous area, but was unable to pick out Regan Linney, and the same two players were involved a couple of minutes later with Linney's cross rattling the post and Cameron Gregory making a brilliant save on the follow-up to deny Kosylo.
United responded strongly and Connor Teale's effort on the spin cleared Caleb Ansen's crossbar, before Jai Rowe saw a header clip the top of the post - with Ansen grabbing the loose ball.
The Pilgrims edged ahead when Hazel showed excellent poise to pick out the run of MAGUIRE, who took the ball down, jinked infield and beat Ansen with a clinical, low left-footed drive from 12 yards.
Ansen subsequently denied Dylan Hill and Hazel to keep Altrincham in the contest at half-time.
Callum Dolan fired narrowly off target for the visitors on the stroke of half-time, but the second half was a cagier affair, with chances at a premium.
Altrincham probably should have levelled in the 72nd minute when substitute James Jones cushioned a neat ball into the box before losing his composure and firing over the top from 12 yards.
United held on relatively stress-free thereafter, as their survival mission stepped up another notch in front of a jubilant Jakemans Community Stadium home crowd.
Boston (3-4-2-1): Cameron Gregory; Connor Teale, Zak Mills, Brad Nicholson; Jai Rowe, Jordan Richards, Greg Sloggett, Cameron Green; Dylan Hill (Olly Green 90), Frankie Maguire (Keaton Ward 78); Jacob Hazel (James Gale 80). Subs (not used): Adam Marriott, Noah Wadsworth, Jacob Scott, Jake Lovelace (gk).
Altrincham (4-2-3-1): Caleb Ansen; Lewis Banks, Charlie Olson (James Jones 68), Lewis Baines, Tylor Golden (Matt Penney 75); Tom Crawford, Elliot Osborne (George Wilson 75); Matty Kosylo (Lucas Weaver 82), Callum Dolan (Kahrel Reddin 65), Alex Newby; Regan Linney. Subs (not used): Isaac Marriott, Harvey Randle (gk).
Referee: Jason Richardson.
Attendance: 2,320 (137 visitors).
PIC: Tim Hoff.