The Pilgrims held the lead three times, courtesy of first half goals from Keaton Ward and Adam Marriott and a further second half effort from Ward.
Harvey Vincent, Luca Thomas and Alfie Cresswell scored Leeds equalisers - with Thomas netting his second and the visitors' fourth five minutes from time to secure victory for the visitors.
Oliver Nicholson, Jude Frostick and Harvey Tomlinson were handed United debuts ahead of kick-off - and the hosts took a 14th minute lead, with WARD rifling home a firm drive from outside the penalty area.
Leeds responded immediately and equalised a minute later with VINCENT tapping home at the back post following a swift raid down the left.
The Pilgrims re-took the lead six minutes before the break, with Ward clipping MARRIOTT away down the left, who shrugged off his opponent, skipped infield and beat Rory Mahady at his near post with a precise, low finish.
The home side held their advantage until the 54th minute when THOMAS crashed home a second Leeds equaliser from 20 yards.
The Pilgrims took the lead for the third time in the 76th minute when WARD stabbed the ball home from 30 yards, having found space in behind the Leeds rearguard, with the onrushing Mahady caught out.
The Whites levelled for once again seven minutes from time, with CRESSWELL glancing home a corner delivery at the back post.
Leeds sealed all three Group C points with five minutes to play when THOMAS rifled home his second of the night.
Boston (4-4-2): Ellis Craven; Oliver Nicholson, Jai Rowe (Billy Bradley 67), Tom Leak, Cameron Green (Ellis Perry-Burdett 60); Dan Mooney (Will Green 74), Keaton Ward, Jude Frostick, Harvey Tomlinson; Adam Marriott (Charlie Burden-Whittleton 60), Pemi Aderoju (Harry Wood 74). Subs (not used): James Owen, Luca Alonzi.
Leeds (4-4-2): Rory Mahady; Alfie Cresswell, Reuben Lopata-White, Jeremiah Mullen, Kristan Moore; Harvey Vincent, Daniel Toulson (Max McFadden 57), Cian Coleman, Coban Bird (Josh McDonald 73); Luca Thomas (Oliver Pickles 89), Rhys Chadwick. Subs (not used): Alex Baird, Louie Dudley, Joseph Billett, Lewis Pirie.
Referee: Jamie O'Connor.
Attendance: 467.
PIC: Chris Bray.