Another home win for Hearts fetched their unbeaten league run to nine games and makes European football almost certain for the Edinburgh side next season.
They fought back from a goal down using their physical strength to overpower a young Dundee side and run out comfortable winners.
Hearts had a couple of good early openings when Paul Hartley missed a gilt-edged chance and then Patrick Kisnorbo headed inches wide from Phil Stamp's cross.
But the misses were costly when Steven Milne fired Dundee in front after only eight minutes racing on to Steve Lovell's pass to curl home a glorious finish.
Hearts tried to hit back and Kevin McKenna was close with both a volley and a header.
But it was Dundee that were creating the chances and Milne shot wide under pressure from Alan Maybury before Lovell missed a great chance with only Craig Gordon to beat.
The Hearts keeper who was called into the Scotland squad this week also produced a great save to keep out Milne's near post flick.
But Dundee were to rue their missed opportunities after the break when Hearts hit them with a triple salvo.
Robbie Neilson's cross was nodded down by McKenna for Hartley to fire home the equaliser after 52 minutes.
And six minutes later, Hearts were in front after Mark Fotheringham fouled McKenna in the box and Hearts skipper Steven Pressley buried the penalty.
Julian Speroni made a good block from Stamp with his legs but the Dundee keeper was helpless as Hearts secured the points after 66 minutes with a third goal.
Neilson's long throw-in was laid off by Dennis Wyness and Joe Hamill poked home a low range shot that Speroni couldn't keep out.