Jai Rowe had handed the Pilgrims a 61st minute lead at Owen Street, only for Elliot Putman to equalise from the penalty spot 13 minutes later.
United scored their first four penalties in the shootout, but Brad Nicholson and Jordan Richards both missed the target as the Pilgrims surrendered a 4-2 lead.
The teams ended with 10 men apiece after debutant Sam Essien and Coalville’s Jake Doyle-Charles were dismissed deep into stoppage time.
It was not an easy afternoon for the Pilgrims, missing first choice strikers Kelsey Mooney and Jimmy Knowles through injury, with stand-in Oliver Wilson suffering a 35th minute dislocated shoulder.
Tom Edge missed a glorious chance at the end of a tight first half, although the Pilgrims did go ahead when ROWE interchanged with Dylan Hill and swept a left-footer past Paul White with 16 minutes of the second period played.
Coalville levelled when PUTMAN converted from the spot after Cameron Gregory had been adjudged to have fouled Wes York.
Essien’s foul in stoppage time sparked a melee - with Doyle-Charles pulling the United midfielder’s hair. He was dismissed - and Essien followed, with two cautions (one for the foul and one for retaliation).
Martin Woods, Michael Bostwick, Ethan Sephton and Keaton Ward were perfect from the spot and despite Tom Leak and Rowe also converting, Nicholson and Richards both cleared the crossbar to send United packing.
Substitute Kieran Cook was the one Raven to miss - also clearing the bar.
Coalville (4-4-2): Paul White; Alex Dean, Herve Pepe-Ngoma, Ashley Carter, Elliot Putman; Terrell Pennant (Wes York 66), Jake Doyle-Charles, Andi Thanoj, Tom McGlinchey; Ashley Chambers, Tim Berridge (Kieran Cook 79). Subs (not used): Jake Hutchings, Luke Shaw, Jake Laban (gk).
Boston (4-3-3): Cameron Gregory; Jai Rowe, Tom Leak, Brad Nicholson, Ethan Sephton; Sam Essien, Jordan Richards, Tom Edge (Martin Woods 88); Dylan Hill (Michael Bostwick 88), Oliver Wilson (Tyler Knowles 35), Keaton Ward. Subs (not used): Will Hall, Ryan Hand, Jake Lovelace (gk).
Referee: Liam Corbett.
PIC: Chris Simpson.