It was a day of celebration in Gorgie as Hearts won the third Edinburgh derby of the season and clinched third place in the cinch Premiership before the split.
Drey Wright's deflected goal inside five minutes had given Hibs the lead but the Jambos responded in style.
Andy Halliday levelled in first half stoppage time, Stephen Kingsley tapped in two minutes into the second half and Halliday added a third after an hour.
There was one change from the side that earned a point last week away to Ross County, with Nathaniel Atkinson coming in for Aaron McEneff.
The Jambos got off to the worst possible start when, on a counter attack, Drey Wright made space in the area and his curled shot took a huge deflection and spun into the corner.
The Hearts play in the opening quarter was disjointed at times and the Tynecastle crowd was anxious, but they should have been level midway through the first half.
Barrie McKay spun superbly on halfway and threaded through a perfect pass for Ellis Simms, who drew Matt Macey out of his goal but dinked the ball just past the post.
Hearts were now firmly in the game after that unsteady start, and came even closer on the half hour when McKay clipped a ball to the back post for Atkinson but the Aussie's header crashed back off the crossbar.
Halliday was next to try his luck when the ball fell to him outside the area but his effort flew over the bar, as the Hibs fans jeered the midfielder.
However, Halliday would be smiling in first half stoppage time when Simms did brilliantly to keep the play alive in the area and force the ball back to Halliday who side footed a shot in off the post.
Hearts carried that momentum straight into the second half and took a deserved lead on 47 minutes. After a corner failed to be cleared by the visitors, Peter Haring's superb cross was tapped in at the back post by Kingsley to send Tynecastle wild.
But that was nothing compared to the scenes just shy of the hour. McKay bamboozled the Hibs defence with a lovely back heel for Halliday who drove for goal and smashed a screamer in off the post from 25 yards.
Hearts were battering their rivals at this point and a superb cross from the excellent Alex Cochrane was nodded just wide by Simms.
A flurry of substitutions by Hibs attempted to add an attacking spark to their play but left them vulnerable to a counter while Hearts were content with what they had, and saw out the three minutes of injury time without fuss to seal a return to Eiropean football for the first time in six years.
Hearts: Gordon, Sibbick, Halkett, Kingsley, Atkinson (Moore '83), Haring, Halliday (McEneff '68), Cochrane, Boyce, McKay (Ginnelly '88), Simms (Mackay-Steven '88). Subs not used: Stewart, Woodburn, Kirk.
Hibs: Macey, Bushiri, Hanlon, Doig (Scott '60), Cadden, Doyle-Hayes (Henderson '70), Newell, Clarke, Wright (Campbell '38), Mueller, Melksersen (Jasper '60). Subs not used: Dabrowski, Hauge, Allan, Stevenson, Delfrriere.