After switching to a back five, Hearts enjoyed heavy possession and struggled to create any chances of note in the first half, with talisman Lawrence Shankland hardly involved in the action.
Zander Clark’s clearing shot immediately preceded him being beaten at the near post for Scott Tiffoney’s opening goal, and was characteristic of a sloppy team performance.
They were outplayed and outplayed by Dundee but looked set to go into half-time just a goal down before a chaotic few minutes saw them lose all discipline.
Gerald Taylor – so imposing against Rangers – was lucky to see only yellow in a wild challenge on Tiffoney, before the Costa Rican defender got up in a tackle and tried to get past Clark on the wrong foot.
Frankie Kent needlessly swung a leg into the box and 1-0 became 3-0 in the blink of an eye.
Steven Naismith showed his displeasure at half-time with a triple substitution, bringing on Yan Dhanda, Malachi Boateng and Yutaro Oda, and it made the difference, but the damage was already done.
Mistakes in their own box before the break were compounded by poor mistakes in the second half.
A day to forget for the Jambos, who will need to improve when they face Falkirk in the League Cup next Saturday.