First half highlights were limited, despite the four bookings handed out by referee Colin Hardie towards the end of the first half, giving a false impression of competitiveness.
In the 25th minute Saints came close when a Paul Sheerin drive was palmed around the post by 17-year-old Dundee keeper Scott Murray.
Jason Scotland got himself into a shooting position four minutes from the interval as he cut in from the left wing, but his final shot was too weak to threaten Murray's goal.
For Dundee, a Bobby Mann free-kick in the 23rd minute was diverted over the cross bar by an agile save from Kevin Cuthbert. Cuthbert also dealt comfortably with a similar free- kick effort from distance by Paul Dixon five minutes short of the interval.
The second period started with a flurry of early action at both ends. John Henry's 46th- minute effort was headed clear by Mann before a Kevin James header was well saved by Murray diving to his right.
Within a minute at the other end of the park, Mann drilled a powerful free-kick for goal that edged just past the post.
There followed a period of inactivity until the 76th minute when Henry's header was blocked by Mann. Two minutes later loud penalty claims from the home side were waved aside when the Saints midfielder Henry appeared to be hauled down by the Dees' defender Paul Dixon.
To cap it all, Neil Janczyk was stretchered off with a leg injury to add to manager Owen Coyle's worries.