Both sides created chances, but it was the Pilgrims who were indebted to goalkeeper Fabian Spiess for denying Jordan Thewlis in a one-on-one scenario after the break, before a brilliant double save in stoppage time to deny Mason Warren and Brendon Daniels.
The result left both clubs well-placed to secure a top five place, albeit with Tamworth and Nuneaton Town still breathing down the Pilgrims' necks.
United had recalled fit-again duo Dylan McEvoy and Jay Rollins to their starting XI ahead of kick-off and looked to soak up their hosts' early attacking forays.
The returning McEvoy and Rollins were involved in the game's first meaningful chance, with the latter's header flying wide following good play involving the former and top scorer Dayle Southwell.
Nat Brown, who had enjoyed a loan spell with Harrogate earlier in the campaign, came to United's rescue with successive goalline clearances to deny Paul Clayton and then Daniels.
There was another massive let-off for the Pilgrims, with Lloyd Kerry's driven shot nestling a fraction wide of Spiess' far post.
United went close themselves six minutes before the break and it needed quick reactions from home keeper Peter Crook to turn Scott Garner's shot behind after Southwell and Rollins had nodded on Kaine Felix's cross.
The second half was a cagey affair, although it was the home side who created the better chances. Clayton has missed a glorious chance when he side-footed wide in the centre of goal while Spiess saved bravely and brilliantly at the feet of Thewlis after the Town sub had galloped through unopposed.
United carved out two clear chances in the dying stages, with Carl Piergianni beating Crook to Grant Roberts' high free-kick but Louie Swain intervened and Southwell fired the rebound too high from a tightening angle.
Crook then made a crucial stop to deny Garner following Zak Mills' torpedo-like throw.
The last word was left to Spiess though, saving low to his right to deny Warren initially and then Daniels as the Pilgrims held on for what could prove to be a vital point in their promotion quest.
Harrogate (4-4-2): Peter Crook; Lewis Turner (Jordan Thewlis 27), Danny Ellis, David McGurk (Luke Foster 46), Louie Swain; Joe Colbeck, Lloyd Kerry, Tom Platt, Brendon Daniels; Paul Clayton, Paul Beesley (Mason Warren 56). Subs (not used): Andy Gascoigne, Paul Thirlwell.
Boston (4-3-3): Fabian Spiess; Zak Mills, Nat Brown, Carl Piergianni, Dylan McEvoy; Scott Garner, Grant Roberts, Lewis Hilliard (Conner Robinson 61); Kaine Felix (Mark Jones 51), Dayle Southwell, Jay Rollins. Subs (not used): Cameron Johnson, Harry Limb, Malachi Lavelle-Moore.
Referee: Anthony Backhouse.
Attendance: 1,027.