Simon Weaver's team had failed to get the better of the O's during four prior attempts, but made it three wins from three this term courtesy of Luke Armstrong's first-half brace.
The big targetman was rewarded for his hard work off the ball as early as the eighth minute. He harried the Orient defence into conceding possession, releasing Alex Pattison, who played the ball right to George Thomson. The latter's cut-back then found Armstrong, who took a touch before poking home inside the six-yard box to break the deadlock.
The Londoners enjoyed plenty of the ball in the period of the contest that followed, but found themselves two goals behind shortly after the half-hour-mark.
Harrogate full-back Lewis Page crossed from the left, picking out Thomson, whose strike at the far post drew an unconvincing save out of Lawrence Vigoroux.
Armstong appeared second favourite to reach the rebound as it rolled across the face of goal, however he showed great determination to get there ahead of two defenders and force the ball over the line.
The visitors made it to the interval without any real scares, Mark Oxley required to make just the one save of any note, keeping out Harry Smith's header.
They were dealt a blow just three minutes into the second period when referee Carl Brook adjudged Josh Falkingham to have diverted Dan Kemp's blast over the top of his own cross-bar with his arm.
But, goalkeeper Oxley came to the Sulphurites' rescue, diving low to his right to keep out Smith's poor spot-kick.
Thomson then saw a curling free-kick clawed out of the top corner by Vigoroux as Town looked to put the game out of reach, though they had already done enough.
Leyton Orient: Vigoroux; James, Beckles, Happe, Ogie (Wood 56); Kyprianou, Pratley; Omotoye (Sotiriou 56), Kemp, Archibald; Smith. Unused substitutes: Byrne, Sweeney, Papadopoulos, Clay, Nkrumah.
Harrogate Town: Oxley; Burrell, McArdle, Hall, Page (Fallowfield 85); Pattison, Kerry, Falkingham; Thomson, Armstrong, Muldoon. Unused substitutes: Cracknell, Smith, Martin, Orsi, Power.
Referee: C Brook.