The Pilgrims accounted for Brackley Town at St James Park - with Elliott handing them a 27th minute lead and Byrne doubling the advantage in first half stoppage time against his old club.
Lee Ndlovu reduced the arrears after half-time and despite having Scott Duxbury red-carded for two cautions late on, the Pilgrims held on for a memorable away win.
With captain Luke Shiels deemed only fit enough for inclusion on the bench and striker Jake Wright Jnr snowed in at home, United boss Craig Elliott recalled defender Scott Garner and top goalscorer Elliott.
The Pilgrims took the game to the hosts, aided by a strong wind, and Elliott blazed wide early on after seizing on a weak Louis Lomas header back.
Marcus Dewhurst saved from James Armson, but it was the visitors who took the lead when ELLIOTT dispatched a bouncing ball with aplomb to give home keeper Danny Lewis no chance.
The Pilgrims doubled their lead in first half stoppage time when BYRNE cracked home a beauty, from outside the box, to swing the tie decisively in United's favour against his former employers.
Brackley cut the deficit three minutes after the break when NDLOVU slammed the ball home from close-range following a lofted cross into the box.
Dewhurst saved brilliantly to deny Ndlovu an equaliser, before Armson smashed the crossbar in stoppage time and Tom Platt heroically nodded an effort off the line as United bravely held on - despite Duxbury's 84th minute red card for two avoidable yellow cards.
Brackley (3-5-2): Danny Lewis; Louis Lomas, Gareth Dean, Glenn Walker; Ellis Myles (Twariq Yusuf 73), Matt Lowe, Shep Murombedzi, James Armson, Connor Franklin (Tre Mitford 79); Lee Ndlovu, Wes York. Subs (not used): Brad Rolt, Jordan Cullinane-Liburd, Jeff Putz, Alistair Worby (gk).
Boston (3-5-2): Marcus Dewhurst; Matt Tootle, Scott Garner, Loick Ayina; Keenan Ferguson (Luke Shiels 83), Paul Green (Kyron Gordon 88), Tom Platt, Shane Byrne, Scott Duxbury; Jordan Burrow, Danny Elliott (Jordan Preston 79). Subs (not used): Fraser Preston, Joe Leesley, Peter Crook (gk).
Referee: Oliver Mackey.
Attendance: 341.
PIC: Glenn Alcock.