United led courtesy of Jan Yeomans' 54th minute header but were denied victory by substitute Scott Ryan's 79th minute leveller.
The result means the Pilgrims must travel to Shropshire on Tuesday evening as they attempt to book their spot in the third qualifying round.
United bossed the first half but were unable to find a breakthrough. Gregg Smith’s early header flew too high following Kabongo Tshimanga’s cross, before the former Milton Keynes Dons striker was unable to turn the loose ball beyond a back-peddling Sam Jones.
Aaron Simms got a crucial touch on Ashley Hemmings’ goalbound free-kick, before Jack Griffiths got back on the goalline to nod Hemmings’ header to safety.
Tshimanga rattled the post on the stroke of half-time while keeper Jones saved efforts from Smith and Tshimanga at the beginning of the second period.
United finally broke the deadlock nine minutes after the break when YEOMANS got up at the back post to power home Hemmings’ corner.
Jones saved well to deny Karl Hawley, while Smith had a firm effort blocked by Simms, and Haughmond levelled with 11 minutes to play.
Carl Rogers nodded down Matt Fletcher’s corner and RYAN angled home a low finish past George Willis.
Willis subsequently stuck out a big hand to claw Steve Hole’s effort to safety following Rogers’ long throw-in and despite Jay Rollins and James Clifton having half-chances at the death, the visitors held on for a replay.
Boston (4-4-2): George Willis; James Clifton, Brad McGowan, Jordan Keane (Liam Wakefield 66), Jan Yeomans; Jay Rollins, Adam Chapman, Jack Thomas, Ashley Hemmings; Gregg Smith (Tyrell Waite 75), Kabongo Tshimanga (Karl Hawley 68). Subs (not used): Jamie McGuire, Brad Beatson, Jack Broadhead, Harry Payne (gk).
Haughmond (4-2-3-1): Sam Jones; George Carpenter, Aaron Simms, Jack Griffiths, Matt Fletcher; Carl Rogers, Dave Howells (Sam Phillips 62); Andy Jones (Scott Ryan 73), Joe Parry (Matt Owen 89), Kevin Renshaw; Steve Hole. Subs (not used): Tom Hewitt, Dan Williams, Luke Thomas, Sean Jones.
Referee: Tom Hancock.
Attendance: 726 (61 visitors).