The Pilgrims were 2-0 victors over Peterborough Sports at PIMS Park to record only their second away league win of the campaign so far.
Leak opened the scoring with a sublime 25-yarder in the 64th minute and Mooney doubled the advantage four minutes later.
It was a hard-earned result for the Pilgrims, missing the services of suspended duo Michael Bostwick and Jordan Richards, the injured Zak Mills and Bermuda-bound Keziah Martin.
United, resplendent in purple, navy and white, were bright from the off and went close to an early lead through Keaton Ward, but he was denied by a flying Peter Crook save.
Dion Sembie-Ferris, back on loan at PSL from Scunthorpe United, blasted an effort into the side-netting for the hosts, but United ended the first half well.
Tom Edge started and almost finished a slick United counter-attack, while Ethan Sephton's 20-yarder grazed the crossbar via a deflection.
The early stages of the second half were end-to-end, but it was the away side who inched in front with 19 minutes of the half played, with Martin Woods setting up LEAK to advance and crash a bouncing 25-yarder beyond the grasp of a diving Crook.
United took a firm grip on proceedings when Jimmy Knowles rolled strike partner MOONEY into the clear and he beat Crook with a composed, low finish from just inside the penalty area.
Gregory excelled to deny Sembie-Ferris in response, while Crook got a touch on Oliver Wilson's angled effort in stoppage time, with the ball bouncing to safety off the post.
Peterborough (4-2-3-1): Peter Crook; Dan Jarvis, Ashton Fox (Sidney Pereira 77), Connor Johnson, Hayden Cann; Dan Lawlor, Oisin Gallagher; Dion Sembie-Ferris, Josh McCammon, Cuba Meyer; Mark Jones. Subs (not used): Hugh Alban-Jones, Harrison Nee, Michael Gash, Lewis Elsom (gk).
Boston (3-4-1-2): Cameron Gregory; Tom Leak, Jai Rowe, Brad Nicholson; Dylan Hill, Tom Edge, Martin Woods, Ethan Sephton; Keaton Ward; Kelsey Mooney, Jimmy Knowles (Oliver Wilson 80). Subs (not used): Sam Essien, Will Hall, Ryan Hand, Tyler Knowles.
Referee: Alex Sawden.
Attendance: 637 (367 visitors).
PIC: Chris Bray.