The Dark Blues shattered Gretna's league record with a physical, tough display that left the Borderers reeling on the ropes - and Rae lead the way with a stunning goal.
They went in front in the ninth minute when keeper Alan Main spilled a cross under pressure and Derek Lyle pounced to smash the loose ball into the roof of the net.
Rae doubled the advantage nine minutes later when he won the ball on the edge of the box and flashed a low 18-yard drive into the bottom corner.
Worse was to follow for Gretna 12 minutes later when Andy McLaren twice saw shots cleared off the line in a scramble but from a resulting corner he spun and volleyed in the third.
Ten minutes before the break Dundee keeper Ludovic Roy pulled off a brilliant one-handed save to keep out Gavin Skelton's 25-yard drive and five minutes later it was game over as Paul Dixon whipped in a cross for Kevin McDonald to send a bullet header crashing in off the underside of the bar.
Dundee shut up shop after the break as Gretna found chances at a premium.
In the 66th minute David Graham whipped over a cross but strike partner Colin McMenamin headed straight at Roy from a good position and with two minutes to go Graham's pace and skill took him into the box but no-one could get on the end of his pullback.