Town raced into a two goal lead with Luke Armstrong and Alex Pattison both making instant impressions on their club debuts.
Rochdale replied after a quarter of an hour through Alex Newby and got themselves back on level terms early in the second half through Conor Grant.
With the scores level heading into injury time, Dale failed to clear a Town corner with Burrell on hand to calmy fire the ball into the corner, sparking wild celebrations from the home stands.
Simon Weaver made two changes from our final pre-season friendly as Ryan Fallowfield and Simon Power replaced Lewis Page and Aaron Martin.
In the Rochdale lineup there were debuts for Corey O'Keeffe, Aidy White and Max Taylor, joining Mark Oxley, Pattison, Rory McArdle and Armstrong in the Town ranks making their first competitive appearance.
After players from both sides were applauded for taking the knee, Town started on the front foot with Armstrong and Josh Falkingham both forcing early saves from Jay Lynch.
Town's fast start resulted in them grabbing the lead after five minutes, Muldoon driving forward and finding his strike partner Armstrong to claim his first goal for the club.
It was two for Town just five minutes later with another debutant getting on the scoresheet as Pattison curled expertly into the far corner to double his side's lead.
The goals continued to arrive in five minute intervals as Alex Newby pulled one back for the hosts, rolling the ball into the bottom corner after a delightful piece of control and nicely weighted pass from Stephen Dooley.
A magnificent solo effort from Power almost kept that trend going as the winger darted down the left before cutting back inside, but fired just over the bar.
Rochdale threatened through an equaliser, but were denied by a smart Oxley save after Jake Beesley had an attempt on the turn, before an important Connor Hall block was needed to deny Dooley.
Weaver's side had the final chance of the half as George Thomson sent a low cross towards Muldoon, whose finish took a deflection as it flashed across goal.
It was Rochdale who made the better start to the second half, with Grant putting them back on level terms inside five minutes, dispatching a pull back from the right into the back of the net.
Town responded well to losing their lead with Pattison seeing a goalbound effort deflect behind for a corner after good hold up play by Armstrong, before Muldoon stung the arms of Lynch with a low drive.
With the scores level heading into injury time, Dale failed to clear a Town corner with Burrell on hand to calmy fire the ball into the corner, ensuring Town started the season with a win.
Harrogate Town: Oxley, Fallowfield (Page 75), Falkingham, Burrell, Thomson, Pattison (Kerry 69), Muldoon, Hall, McArdle, Armstrong, Power
Subs not used: Smith, Martin, Orsi, Cracknell
Goals: Armstrong 5, Pattison 10, Burrell 91
Booked: Pattison, Burrell
Rochdale: Lynch, O'Keeffe, White (Graham 66), Mcnulty, Taylor, Dooley, Morley, Beesley, Newby, Grant (Broadbent 77), Odoh (Cashman 71)
Subs not used: Done, Brierley, Dunne, Coleman
Goals: Newby 15, Grant 51
Booked: Beesley, Odoh
Referee: A Coggins