Defender Ryan McGowan headed in a Danny Grainger corner from close range to put Hearts in front after 27 minutes before forward Skacel netted with a trademark left-footed strike from 25 yards after 53 minutes and sealed victory with an 89th-minute third.
The victory ensured sixth-placed Hearts could not be caught by Kilmarnock, whose loss in Paisley saw St Mirren relegate the Dons to ninth place.
After a 13-match unbeaten run, fellow Scottish Cup semi-finalists Aberdeen have now lost three successive matches and have not won in seven SPL fixtures - since defeating Dunfermline 1-0 in January.
The one bright spot was Russell Anderson's first appearance since leaving for Sunderland in June 2007, putting him on course for a Scottish Cup semi-final place against Hibernian in two weeks' time.
Hearts have two possible routes to Europe in front of them, with the sizeable object of holders Celtic in their Hampden clash.
Hearts, whose players this week received their overdue March wages, might have secured their top-six place sooner, but lost 2-1 at St Johnstone last weekend.
Manager Paulo Sergio was able to recall Craig Beattie, Ian Black, Jamie Hamill and Skacel, with goalkeeper Jamie MacDonald named to start despite going off with a hip injury in Perth.
MacDonald was little more than a spectator for much of the opening 45 minutes against a blunt Dons attack.
Black cut in from the left and shot wide across goal after 11 minutes, Darren Mackie headed over for Aberdeen and Kari Arnason, on trial with Hearts last summer, shot tamely wide.
Hearts appeared the more threatening, but were off target with their passing in the final third and Grainger wasted a free-kick from a promising position.
The left-back soon made amends as his inswinging corner to the far post found McGowan to head in from close range.
A long throw from Arnason troubled the Hearts defence, with Andy Considine heading down for Peter Pawlett, who appeared unaware as the ball bounced in front of him and a defender cleared.
A Pawlett corner found Considine running towards the near post, but the defender's shot was blocked by Beattie, who then scuffed a shot from the edge of the box at the other end.
A low Andrew Driver cross from the left evaded everyone, including Skacel, as Hearts resumed on the attack.
Hearts soon had a second as McGowan found Skacel and the forward punished the Dons for giving him space, drilling a left-footed shot into the top corner from 25 yards.
The Dons last scored twice in the SPL on January 2 and it appeared more likely Hearts would score again than their visitors.
Driver could only weakly glance a header from a McGowan long throw and Sergio felt comfortable enough to take off Black 22 minutes from time. The key midfielder has been nursing a hernia and was replaced by Suso Santana.
Santana soon had an impact. He ran at Dons left-back Clark Robertson and crossed for Skacel.
The forward's attempt to divert the ball goal-wards from six yards appeared to hit Rory McArdle on the arm, with Considine also in close attendance. There were muted appeals from Hearts and the Dons survived.
Former Scotland defender Anderson came on for the final 14 minutes, making his second Dons debut and taking the captain's armband from Considine.
Aberdeen's woes continued, though, as Vernon shot over on the turn from close range before the visitors failed to clear and Skacel pounced, tucking in to seal victory.