Broadhead's 13th minute breakthrough at AFC Mansfield on Saturday afternoon set the tone for a dominant United performance, with the previously unbeaten hosts finding the Pilgrims a tough nut to crack.
Tshimanga sealed the victory with a well-taken second five minutes into stoppage time at the end of the game.
The Pilgrims edged in front after debutant Shane Killock had kept alive James Clifton’s deep corner. Killock’s shot was blocked and BROADHEAD swept home his first goal for the club from 12 yards.
United needed all hands to the pump to repel the long throws of ex-Pilgrim Connor Smythe, who was providing the home side’s main ammunition.
Further chances for Boston fell to Brad McGowan and Jamie McGuire, but experienced keeper Jason White was not unduly troubled on either occasion.
Killock was in the right place at the right time to deny Cameron Dear from distance as United went into the break with a one-goal lead.
Smythe and Craig Mitchell fired efforts off target for the Bulls after half-time, while White sailed home an extraordinary free-kick from the halfway line with nine minutes to play but the home side were penalised for offside players interfering with George Willis.
Jay Rollins was denied by White, while Clifton sailed an effort narrowly wide, before the Pilgrims finally clinched their progress in the fifth minute of added time.
TSHIMANGA terrorised ex-Pilgrim Matt Wilson before weaving into the box and finishing with aplomb past White.
AFC Mansfield (4-2-3-1): Jason White; Liam Marsden (Matt Plummer 5), Jordan Annable, Matt Wilson, Connor Smythe; Jonathan D'Laryea, Phil Buxton; Oliver Fearon, Jimmy Ghaichem, Cameron Dear; Craig Mitchell (Nick Guest 74). Subs (not used): Lynton Karkach, James Cullingworth, Elliott Wall, Joe Cheeseman, Charlie Dixon (gk).
Boston (4-4-1-1): George Willis; Liam Wakefield, Brad McGowan, Shane Killock, Jan Yeomans; James Clifton, Jamie McGuire, Jack Broadhead, Jay Rollins; Jack Thomas; Gregg Smith (Kabongo Tshimanga 66). Subs (not used): Ashley Hemmings, Adam Chapman, Karl Hawley, Brad Beatson, Jordan Keane, Harry Vince.
Referee: James Oldham.
Attendance: 613.