The home team made a flying start and were 1-0 up inside two minutes when Kevin McDonald's 20-yard shot beat Chris Smith with the aid of a deflection.
As the visitors started to put a bit of pressure on the home defence, Stewart Kean twice went close just after the half hour mark. Firstly her failed to connect with a low cross when just two yards out before Kelvin Jack denied him from 12 yards.
Steven Craig almost doubled Dundee's lead five minutes before the break when Kirk Broadfoot raced back to boot the ball off the line after Craig had stroked the ball towards an open goal.
A cracking left-foot free-kick by Paul Dixon from 25 yards was heading into the top corner until Chris Smith dived full length to tip the ball over after 58 minutes.
World -up bound goalkeeper Kelvin Jack saved Dundee twice in quick succession when he turned Stewart Kean's effort around the post before tipping Charlie Adam's cracking 40-yard shot over the bar.
Dundee substitute Craig O'Reilly made a storming entrance when he scored twice from close range within 10 minutes of coming on, his goals coming in the 73rd and 77 minutes.
Seven minutes from time another sub, Andy Ferguson, capped a fine display from the home team when he scored the fourth two minutes after coming on.