The duo struck on 49 and 70 minutes respectively as the Pilgrims recorded a thoroughly deserved away victory.
United had started well at the Tameside Stadium and had already seen a number of presentable chances go begging before Jones' breakthrough four minutes into the second period.
New signing Fabian Spiess was handed his United debut, while Jones replaced the injured Kaine Felix.
For the second week running, John Sands was presented with a great chance inside the opening seconds but after being played through by Jones, he blasted wide from 18 yards.
Jones' header flew wide for the Pilgrims following Hilliard's deep cross before Jones was booked for simulation after referee Iain Turner deemed he had dived in the box with United furiously claiming a penalty.
Jones' action-packed opening continued when he fired over following Jay Rollins' left-wing cross.
Spiess was called upon to make a crucial stop to keep out a Joe Guest effort at his near post in a rare Curzon attack.
Hilliard volleyed marginally over Hakan Burton's crossbar following a Grant Roberts corner, while United wanted a penalty for Alex Brown's tangle with Roberts but referee Turner was once again unmoved.
United started the second period brightly and were rewarded four minutes into the half with JONES thumping home a low 25-yarder following good build-up play involving Hilliard and Liam Marrs.
Curzon tried to respond and Matt Warburton's fierce cross-shot evaded everybody and went out for a throw to Boston, before the same player shot wide of the near post following Ryan Brooke's cross from the right.
United killed off the contest with 20 minutes to play when Jordan Richards won possession to advance and free Roberts, who in turn played in HILLIARD to beat Burton on the angle with the ball eventually crossing the line.
Curzon (4-4-2): Hakan Burton; Chris Rowney, Jonathan Hunt, Danny Shaw, Connor Hampson; Jordon Wright, Alex Brown, Liam Tomsett, Joe Guest (Michael Norton 77); Ryan Brooke (Niall Cummins 77), Matt Warburton. Subs (not used): Tom Eckersley, Simon Woodford, Cameron Mason (gk).
Boston (4-4-2): Fabian Spiess; Zak Mills, Scott Garner, Carl Piergianni, Liam Marrs; Lewis Hilliard, Jordan Richards, Grant Roberts, Jay Rollins; Mark Jones, John Sands (Cameron Johnson 73). Subs (not used): Ryan Robbins, Conor Green, Kofi Ross, Jason Alexander (gk).
Referee: Iain Turner.
Attendance: 377.