The visitors arrived in North Yorkshire without a win in six matches though they began the afternoon brightly and were ahead in the 14th minute, Tom McDonnell ramming home Luke Wanadio’s cross from the left.
Gerry McDonagh’s delicate chip almost made it two soon afterwards, but Harrogate goalkeeper James Belshaw denied him brilliantly.
Harrogate restored parity just past the half-hour-mark, Callum Howe nodding Joe Leesley’s free-kick across goal and, although Dominic Knowles was denied on the goalline, Burrell followed up from close range.
The game was turned on its head nine minutes into the second period, Burrell meeting a right-wing corner by Leesley at the near post to head home.
The same pair combined again to wrap up the points as Burrell stooped to get on the end of Leesley’s free-kick and completed his hat-trick.
Jack Muldoon put a gloss on the scoreline in stoppage-time, controlling Belshaw’s long ball over the top before confidently bending his 10th goal of the season into the top corner of the net.
Harrogate, who overcame the Shots 2-0 away back in August, move to within four points of the National League summit.
Ten-man FC Halifax Town came from a goal down to earn a hard-fought 1-1 draw at Dagenham & Redbridge thanks to Nathan Clarke’s equaliser.
Josh Staunton was sent off at his former club after 35 minutes during which the visitors had kept Dagenham quiet.
From that point the Shaymen were forced to try to claw something from the game against the odds.
Their task was made even harder when Jack Munns scored on the hour mark, but Halifax’s fighting spirit was rewarded when Clarke rose brilliantly to head in a corner with 10 minutes to go.
Dagenham also finished the game with 10 men when captain Ben Nunn got a second booking.
A poor first half had only beenbrought to life when Staunton was dismissed 10 minutes before the interval.
The former Dagenham man lunged for the ball and caught Alex McQueen near the halfway line after winning it.
The challenge looked reckless, but whether it was of sufficient force and malice to warrant a red rather than a yellow was unclear on one sighting.
Halifax could hold out no longer than the hour mark when Munns found a yard of space on the left of a crowded penalty bo and drilled a shot back across goal into the top right corner.
But the hosts were made to pay for not making more of having the upper hand when Clarke met Sellers’s corner with a terrific header at the far post.
Dagenham captain Nunn was then sent off for a second caution in added time.