A 20th minute strike from Hearts captain Colin Cameron was enough to earn the points for the Tynecastle side.
Aberdeen ran them close and can consider themselves a little unfortunate not to have earned a draw.
Aberdeen put the Hearts defence under pressure early on and won a free-kick outside the box when Scott Severin went in late on Derek Young.
The resulting kick found its way to Ben Thornley but his effort was blocked by the Hearts defence.
Hearts skipper Colin Cameron had a long range effort after 10 minutes following good work from Fulton and Mahe but the midfielder failed to find the target.
Cameron's luck was in 10 minutes later, however, when he thundered Hearts into the lead from just inside the box after a McKenna knock down.
Hearts were buoyed by Cameron's strike and began to knock the ball around purposefully.
However Aberdeen still posed a threat and after 26 minutes Tomaschek was forced to head over his own bar after another good delivery from Thornley.
A mistake by Severin then gave Derek Young a chance to shoot but Antti Niemi saved well.
Eight minutes before the break Steve Fulton engineered an opening for himself with a tremendous run at the Dons defence but his shot hit the side netting.
On the stroke of half-time, Gary Wales squandered a glorious chance to extend Hearts' lead, volleying over the top from close range after a knockdown from McKenna.
Hearts slowed the game down in the second half but Aberdeen attempted to keep up the pressure in their search for an equaliser.
Bisconti found Darren Young on the edge of the box and although the young forward turned well, his shot from 18 yard was easily taken by Niemi.
There was a scare for the Dons in the 67th minute when goalkeeper David Preece conceded a corner after failing to clutch an in-swinging cross from Hearts' substitute McSwegan.
Cameron almost snatched a spectacular second for Hearts seven minutes from time.
He reacted quickly to a punched clearance from Dons goalkeeper David Preece and attempted a speculative bicycle kick which flew just over the bar.
Three minutes later the Hearts captain had a more conventional opportunity to secure their win, but skewed the ball badly wide after eluding the Dons defence.
Aberdeen put a lot of effort into the game but ultimately were unable to breach the Hearts defence.
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Saturday, 4 August, 2001, 17:58 GMT 18:58 UK
Hearts edge out Aberdeen
Hearts 1-0 Aberdeen
A 20th minute strike from Hearts captain Colin Cameron was enough to earn the points for the Tynecastle side.
Aberdeen ran them close and can consider themselves a little unfortunate not to have earned a draw.
Aberdeen put the Hearts defence under pressure early on and won a free-kick outside the box when Scott Severin went in late on Derek Young.
The resulting kick found its way to Ben Thornley but his effort was blocked by the Hearts defence.
Hearts skipper Colin Cameron had a long range effort after 10 minutes following good work from Fulton and Mahe but the midfielder failed to find the target.
Cameron's luck was in 10 minutes later, however, when he thundered Hearts into the lead from just inside the box after a McKenna knock down.
Hearts were buoyed by Cameron's strike and began to knock the ball around purposefully.
However Aberdeen still posed a threat and after 26 minutes Tomaschek was forced to head over his own bar after another good delivery from Thornley.
A mistake by Severin then gave Derek Young a chance to shoot but Antti Niemi saved well.
Eight minutes before the break Steve Fulton engineered an opening for himself with a tremendous run at the Dons defence but his shot hit the side netting.
On the stroke of half-time, Gary Wales squandered a glorious chance to extend Hearts' lead, volleying over the top from close range after a knockdown from McKenna.
Hearts slowed the game down in the second half but Aberdeen attempted to keep up the pressure in their search for an equaliser.
Bisconti found Darren Young on the edge of the box and although the young forward turned well, his shot from 18 yard was easily taken by Niemi.
There was a scare for the Dons in the 67th minute when goalkeeper David Preece conceded a corner after failing to clutch an in-swinging cross from Hearts' substitute McSwegan.
Cameron almost snatched a spectacular second for Hearts seven minutes from time.
He reacted quickly to a punched clearance from Dons goalkeeper David Preece and attempted a speculative bicycle kick which flew just over the bar.
Three minutes later the Hearts captain had a more conventional opportunity to secure their win, but skewed the ball badly wide after eluding the Dons defence.
Aberdeen put a lot of effort into the game but ultimately were unable to breach the Hearts defence.
Hearts: Niemi, Severin, Mahe, Webster, Boyack, Tomaschek, Cameron, McKenna, Fulton, Wales, Adam.
Subs:
Aberdeen: Preece, Guntveit, McGuire, Whyte, McNaughton, Darren Young, Mackie, Bisconti, McAllister, Derek Young, Thornley.
Subs: Esson, Rutkiewicz, Solberg, Tiernan, Bett.
Referee: Bobby Orr