Macauley Bonne opened the scoring in the 23rd minute before a brace from veteran McAnuff either side of half-time killed off the hosts.
Both sides went into the match boasting unbeaten records, but it was the visitors who started the brighter.
Orient capitalised on an excellent advantage played by referee Marc Edwards to go in front as Charlie Lee played in Bonne to finish past James Belshaw.
Belshaw was beaten again in the 36th minute, saving from Josh Koroma but only succeeding in pushing the ball out for McAnuff to tap home.
Harrogate regrouped and finished the half strongly, Bonne clearing Liam Kitching's header off the line and Dean Brill doing well to keep out Kelvin Langmead.
But Orient killed off Harrogate in the 68th minute when McAnuff fired home Koroma's cut-back to take the visitors a point clear of their opponents at the top.
Elsewhere, referee Daniel Middleton sent-off Matty Brown and Matty Kosylo as nine-man FC Halifax Town lost 2-1 at home to Hartlepool.
The contest was set-up for an intriguing second-half, but Middleton took centre stage with some highly contentious decisions as he dealt Town a double blow of sending off Brown and awarding Pool a penalty shortly after half-time.
The dismissal of Kosylo was perhaps less debatable after a robust challenge near the halfway line to earn him his second booking.
Hartlepool had been the better side in the first-half, but there had been enough evidence to suggest Town will have fancied their chances of their first win in five before Town's two red cards in four minutes helped consign The Shaymen to their first home defeat of the season thanks to goals from Liam Noble and Nicky Featherstone.
Jacob Hanson raised late hopes of what would have been a thrilling comeback as Town commendably hit back, despite the circumstances.
Liam Noble twice went close to scoring for Hartlepool in an impressive first-half, hitting the bar and drawing a superb save from Sam Johnson with long-range efforts.
Scott Loach did well at the other end to keep out a close range Jonathan Edwards effort and Jordan Preston's vicious shot across goal.
The game completely changed a few minutes into the second-half when referee Middleton sent-off Brown and awarded Hartlepool a penalty - both controversial decisions and both leaving most, if not all, inside The Shay, mystified as to why.
The two big decisions rubbed salt into the wound for Town, who will have felt harshly treated by Middleton, who moments earlier, had not given a foul for a budge by Davies on Kosylo, only to award Hartlepool a free-kick seconds later for a soft-looking push.
From that free-kick came the penalty, after Peter Kioso had met it with a diving header four yards out that was straight at Johnson.
There was barely time to digest what had just happened when Kosylo was shown a second yellow for a poor tackle in the middle of the pitch, clearly still aggrieved at Brown's dismissal and the penalty.
Hartlepool made their advantage count when Featherstone arrowed a superb shot into the top corner after cutting in on his left-foot on the edge of the area.
But Town didn't crumble, responding in spirited fashion and launching the odd attack.
The biggest cheer of the afternoon was reserved for the booking of Kioso with 15 minutes left, until Hanson produced a calm finish to set-up a dramatic climax when he raced onto Preston's pass after the Town man had run from one box to another in lung-busting style.