Burrow touched the ball home from close-range after Jake Wright's header had been palmed on to the post by Dino Visser.
The Pilgrims had earlier fallen behind to Ryan McLean's low drive three minutes into the second half.
With Tom Nixon back from suspension and Finley Thorndike handed a full debut, United showed two changes to the side which had defeated Leamington last time out.
Billy Chadwick, looking to build on his stunning goal a week previously, sailed an early, opportunist 30-yarder narrowly wide, before teeing up fellow Hull City loanee Nixon to test Dino Visser from distance.
Hereford's response was strong, primarily through left-sider Miles Storey, and Luke Shiels had to clear off the line to deny Dan Jarvis.
Hereford, led by Zak Lilly, had to produce two goalline clearances to thwart Thorndike and then Burrow after Visser had been unable to deal with Nixon's initial cross from the right.
Cameron Gregory kept the shoreline level with a save inside 15 seconds of the restart, denying Storey at the back post, but the Bulls did edge in front three minutes after the break when McLEAN weaved through before finishing low into the far corner from 18 yards.
The Pilgrims produced their best spell of the game - and Thorndike went close to an equaliser, but lost composure 20 yards from goal after working the perfect shooting opportunity.
United's leveller duly arrived 12 minutes from time when Chadwick crossed from the right, Wright saw his header clawed on to the woodwork by Visser and BURROW scrambled the loose ball home from no more than a yard out.
Visser subsequently denied Chadwick from long-range, before getting all the way behind substitute Tre Mitford's header, only for Ryan Lloyd to rattle the post with virtually the last kick of the game for the hosts.
Hereford FC (4-2-3-1): Dino Visser; Jared Hodgkiss, Aaron Amadi-Holloway, Zak Lilly, Sean Lawton; Luke Haines (Ryan Lloyd 60); Dan Jarvis (Jethro Hanson 62); Ryan McLean, Harry Pinchard, Miles Storey; Tyrone Barnett (Jack Holmes 82). Subs (not used): Orrin Pendley, Jamie Egan.
Boston (4-1-2-1-2): Cameron Gregory; Tom Nixon, Luke Shiels, Ben Pollock, Ethan Sephton; Tom Platt; Zak Mills, Sam McLintock; Finley Thorndike (Jake Wright 65); Jordan Burrow (Tre Mitford 82), Billy Chadwick. Subs (not used): Keenan Ferguson, Will Atkinson, Lirak Hasani.
Referee: Harry Jones.
Attendance: 1,505 (104 visitors).
PIC: Steve Niblett.