Hearts 3-0 St Mirren
St Mirren's relegation torment continues at least for another 24 hours after a thorough beating by Hearts.
Needing a point to ensure Dundee finish bottom, the nervous Buddies fell behind to a blistering strike off the underside of the bar by Jamie Walker.
Kevin McHattie then squeezed a 25-yard free-kick under goalkeeper Craig Samson just before the break.
Jamie Hamill ended hopes of a second-half revival from the penalty spot as Kenny McLean was sent off.
And it means that Dundee will entertain Aberdeen knowing that victory will keep their hopes of a great escape alive for another week.
The cold winds of financial woes continue to swirl around Tynecastle and the home side had to cope with the absence of suspended captain Andy Webster and injured on-loan Liverpool striker Michael Ngoo.
But a youthful Hearts were on fire from the kick-off, inspired by a red-hot atmosphere generated by a near-capacity crowd thanks to cut-price admission.
Fear rather than blood appeared to be running through Buddies veins as John Sutton sent an early strike just wide and a powerful Jason Holt drive almost punctured goalkeeper Craig Samson's chest.
St Mirren, though, should have taken the lead following a cleverly-worked free-kick.
Steven Thompson peeled off cleverly at the back post to head a Gary Teale cross into the path of Lee Mair, but the experienced defender could only find the upper tiers of the packed stand with his half-volley under pressure.
Hearts almost immediately switched play to the other end to take the lead.
Walker gathered 35 yards from goal, thrust past a couple of challenges then unleashed a howitzer off the underside of the crossbar.
With St Mirren's nerves and tempers on edge, manager Danny Lennon showed tactical bravery by hauling off yellow-carded full-back David van Zanten five minutes before the break, with Sam Parkin forming a three-man front line.
That briefly sparked the Buddies into life, but they found themselves two behind when McHattie's low free-kick slipped under a suspect-looking Samson.
With the strong wind now at their backs, St Mirren did hint at a second-half comeback.
Conor Newton, having been switched from midfield to right-back, evaded a couple of challenges before forcing goalkeeper Jamie MacDonald to parry clear and a Parkin header was cleared off the line by Holt.
However, the Buddies' fate was sealed when McLean challenged McHattie and the result was a penalty that looked harsh in itself even without the resulting red card.
Hamill's spot kick arrowed into the corner and Buddies' hearts.
Paul McGowan forced a save from MacDonald and Teale's chip on the rebound was headed off the line by Darren Barr.
There was still time for Hamill to rub salt in Saints wounds with another clearance off the line from a Thompson header.
Three was enough for Hearts, with Parkin's bloodied nose symbolic of a bruising day for a Paisley side still that one point short of ensuring Scottish Premier League safety.