A George Thomson first half header put Town ahead, before Jordan Thewlis' second half brace put Town out of sight.
Last season's top scorer Simon Ainge was unlucky to see his header bounce back off the bar earlier on, but then added to the score-line with an 82nd minute penalty to finish the scoring.
Simon Weaver named six summer signings in his first XI of the season with James Belshaw, Ryan Fallowfield, Ben Middleton, Josh Falkingham, Thomson and Thewlis all involved from the off.
Both sides looked to make a fast start to the contest as Ashley Chambers shot over the bar, while Jack Emmett's shot at the other end took a deflection before rolling into the arms of Tyrell Belford.
It was Town who grabbed the advantage though as Thomson's headed Joe Leesley's corner in from close range after 17 minutes.
The provider of Town's first then had the chance to double his side's lead, but could only find the side netting after Fallowfield's cross found its way to the back post.
A neat piece of skill from Thewlis that beat two players almost saw Town go two goals to the good soon after, but Belford claimed the shot.
On the stroke of half time Chambers had a golden chance to send the sides in level after collecting a long ball and rounding Belshaw, though the visiting striker somehow managed to find the side netting with only Warren Burrell to beat on the line.
Ainge was desperately unlucky not to add his name to the score sheet in the first action of the second half as he headed Thomson's pinpoint cross back off the bar.
Town's lead was doubled on the hour mark as Middleton's attempt from Leesley's corner fell kindly to Thewlis on the goal line to finish.
Six minutes later Thewlis claimed his second of the afternoon as the forward looked to have flicked Leesley's inswinging free kick past Belford and in.
After a flowing move ended in jack Emmett being brought to ground inside the area, Ainge put the final nail in the Nuneaton coffin smashing home from the spot with eight minutes to go.
Harrogate Town: Belshaw, Fallowfield, Parker, Falkingham, Middleton, Burrell, Emmett (Vann 83), Thomson, Ainge, Thewlis, Leesley
Subs not used: Kennedy, Cracknell, Lees, Day
Goals: Thomson 17, Thewlis 60, 66, Ainge (p) 82
Nuneaton: Belford, Trotman, C Wildin, Scott (Tweed 53), Gascoigne, Heaton, Beswick (Nicholson 53), Daniels, Chambers, Hickey, Ball (Brennan 74)
Subs not used: L Wildin, Taylor
Booked: Beswick, Scott, C Wildin
Referee: T Parsons