A sentimental decision paid off spectacularly for Hearts boss Craig Levein as the Edinburgh club secured third place in the SPL and a UEFA Cup spot next season.
With 20 minutes to go, and the match still goalless, Frenchman Stephane Mahe was brought on to make his farewell appearance before retirement and, within eight minutes, the full-back had crossed for Mark De Vries to head home the winner.
The result halted a run of three defeats for Hearts although Dundee were clearly saving themselves for next week's Scottish Cup final.
Hearts were quickly into their stride and dominated possession without seriously threatening until the 12th minute when Joe Hamill's low cross from the left was met by the diving De Vries who headed narrowly wide.
The big Dutchman then beat the offside trap but a poor first touch enabled defender Lee Mair and keeper Julian Speroni to clear the danger.
Almost immediately a long ball from Gavin Rae split the home defence only for striker Steve Lovell to find the side-netting with his left foot.
Hearts kept pressing with full-back Alan Maybury twice going close from long range but a mix-up between Robbie Neilson and skipper Steven Pressley almost let Lovell in again shortly before half time.
The second period began controversially as Dundee striker Nacho Novo appeared to handle the ball inside the penalty area but experienced referee Willie Young felt it was accidental.
For the most part Hearts were forced to shoot from outside the box and it was from there that Neil MacFarlane finally produced the first shot on target after 61 minutes.
Hearts really should have taken the lead nine minutes later, but after De Vries had set him up perfectly, substitute Gary Wales somehow scooped the ball wide from six yards.