From kick off it became very evident both sides wanted a good start to the season and both quickly settled into passing, attacking football.
The best opening effort came from Whitby in the 14th minute, when a quickly taken free-kick to Whitby's new signing, Mark Tinkler, saw his 20-yard effort fly narrowly over the Buxton bar.
But it was the visitors who took the lead in the 21st minute when a deep corner was headed back across the area and the Buxton captain, Mike Towey, headed home from seven yards.
The Derbyshire side continued to pressurise Whitby and Gavin Knight should have capitalised on his effort eight minutes later, only to see his shot go into the side netting.
Within a minute, he had a free chance to increase the lead and this this time his shot went three yards wide.
Whitby also went near with a close range header from Tom Raw which flew past the right hand post.
In the 35th minute, a lovely passing move by the visitors, ended with a stinging shot from Scott Maxfield from 25 yards out, bringing an acrobatic, flying save from Ben Escritt in the Whitby goal.
Whitby moved up a gear for the last 10 minutes of the half, but failed to break down the solid Buxton defence.
In the 52nd minute, Whitby were awarded a free-kick 20 yards out, which was bent around the wall by Steve Huggins, only to see it fly inches past the left post and the well beaten Scott Hartley in the Buxton goal.
On the hour, Whitby replaced Lee Nogan and Shaun Ross with Andy Burton and impressive youngster Sam Garvie, who with his first touch soon afterwards, turned at the edge of the area and chipped his shot a fraction over the bar, to the agony of the expectant home fans.
Midway through the second half, again following a neat Whitby build-up, Karl Charlton turned on the edge of the Buxton box and his low shot through the defenders legs was well held by the unsighted keeper Hartley.
Both teams appeared to cancel each other out for a 15-minute period before the visitors ensured they took all three points when, in the 89th minute, Buxton's man of the match Knight collected the ball and drilled it past Escritt from 25 yards.
Whitby will have been disappointed not to get something from the game, but on balance, the score reflected the match and none of the home supporters could complain at the end result.
Whitby Town: Escritt, Pallender, Burgess, Nogan (Burton 60), Forster (capt), Tinkler (Thompson 81), Huggins, Ross (Garvie 60), Raw, Brunskill, Charlton. Subs not used: Lyth, Ledgeway.
Match ball sponsor's man of the match (for Whitby): Tom Raw
Attendance: 359.
Result: Whitby Town 0 Buxton 2