Dons striker Niall McGinn came closest to breaking the deadlock, but was denied by the woodwork in the second half.
The first major talking point came when referee Steven McLean booked Nigel Hasselbaink after the St Johnstone forward went down looking for a penalty following a challenge from Russell Anderson.
Saints were then denied the lead when Dave Mackay drove a free-kick from the corner of the area towards Jamie Langfield's goal which the goalkeeper tipped over.
Aberdeen responded when Gregg Wylde forced Steve Banks into a full-stretch save with a flicked volley from a Mark Reynolds cross.
Hasselbaink then set up Murray Davidson with a cutback from the right, but the midfielder fired a shot over the bar with the goal at his mercy.
Banks again showed great agility for a 41-year-old to turn away a powerful Cammy Smith drive and seconds later the ball was worked to Josh Magennis who sent a low strike wide of the upright.
The Dons began to look stronger and a long pass from Clark Robertson dropped kindly for McGinn, and he smashed a half-volley off the crossbar.
Wylde was again denied, this time by Tam Scobbie's last-gasp lunge, and a minute later McGinn worked space to curl a strike from 20 yards, but Banks threw himself across goal to pull off a stunning save.