Two goals from Kris Boyd left the Rangers striker top scorer with 20 goals, even though he only joined the club in January.
There was also time at the end for a warm ovation for Alex McLeish even though a fair number of the home support had departed by then.
In a match which was meaningless in terms of league placing, Hearts made nine changes from their midweek clash against Aberdeen but it nevertheless turned out to be an entertaining encounter.
Rudi Skacel shot narrowly wide in the opening minute and Dado Prso volleyed past the post for the home team.
Ronald Waterreus made an excellent save from Michal Pospisil before the referee incurred the wrath of the home fans.
Prso managed to shrug off the attentions of Martin Petras before advancing on the Hearts keeper only for the referee to award Rangers a free-kick outside the box, which was little consolation.
Rangers took the lead when the unmarked Boyd headed home a Peter Lovenkrands corner at the back post nine minutes before the break.
Waterreus saved well from Pospisil and Mirsad Beslija as Hearts searched for an equaliser at the start of the second half.
The Rangers keeper again came to his team's rescue to block a close-range Skacel shot with his feet and then threw himself full length to deny substitute Lee Johnson's powerful strike.
Having survived this pressure Rangers went further ahead when Boyd was on hand to steer home a perfect Gavin Rae cross and at least grant McLeish a victory in his last match.