Matt Lockwood's first-half free-kick saw a dominant Dundee secure their first home win of the season as Hearts dropped to ninth in the league.
Colin Nish spurned two chances to double his side's lead just before half-time, Marius Zaliukas thwarting the Dundee striker's attempts.
The visitors pressed for an equaliser but it was the home side who looked closest to scoring in the second half.
And neither side could add to Lockwood's curling effort.
Dundee went ahead in 21 minutes when Lockwood fired in a spectacular free-kick from the edge of the 18-yard box.
His left foot shot curled high over the wall and rattled past Jamie MacDonald at his left side just inside the junction of the goal.
Mehdi Taouil threatened to reply for Hearts with a stinging drive which Rab Douglas thwarted with the heel of his hands and then, five minutes later, the Dundee keeper leapt full length to his left to palm a blistering Arvydas Novikovas free-kick away for a corner.
Colin Nish had two good chances to add to Dundee's lead. The first opportunity came just before half-time, when he rounded the Hearts keeper and fired a shot from 18 yards only for Marius Zaliukas to block the attempt.
The Hearts defender thwarted Nish again just after the hour mark, deflecting his shot for a corner.
In the 71st minute Dundee sub John Baird, only minutes on the field, swivelled onto a long ball in the Hearts box to force MacDonald into a sprawling save at his right-hand post.
Hearts though, maintained a barrage of pressure and Zaliukas nodded powerfully over from six yards as full-time neared and then in the last minute of normal time found Douglas well positioned to safely clutch another strong headed effort.
Dundee hung on to take their seventh point of the Scottish Premier League season and only their second win, both victories having come against Hearts.
Dundee's youthful central defensive pairing of Declan Gallagher and Kyle Benedictus were imperious throughout, while Nicky Riley's lung-bursting runs and availability for the out ball were firm reminders that sometimes professional players really do play for the jersey.
A deserved win for a Dundee side who drained themselves of every ounce of effort while Hearts will rue a performance which never matched their midweek efforts 100 yards down the road at Tannadice, where they beat Dundee United on Wednesday to reach the semi-finals of the Scottish Communities League Cup.