Niall McGinn struck the crossbar and also had a shot saved brilliantly by veteran Saints goalkeeper Steve Banks.
The result means St Johnstone stayed a point above their opponents in the early league standings.
Both sides were looking to bounce back from morale-sapping defeats in their last league outings, the Dons having lost to 10-man Hearts while St Johnstone were beaten 4-0 by Tayside rivals Dundee United.
The home side showed four changes from the side that won on penalties against Alloa in a midweek League Cup tie. Willo Flood and Jonny Hayes suffered injuries in that match, and were replaced by Michael Hector and Gregg Wylde. Joe Shaughnessy returned after being rested, while Josh Magennis came in for Calvin Zola.
Saints made two changes to the side beaten by United, as Paddy Cregg and Stevie May dropped to the bench, with Chris Millar and former Aberdeen player Gary McDonald coming into the side in their stead.
Both sides started positively, and after eight minutes it took a fine intervention from Frazer Wright to prevent Magennis opening the scoring from Peter Pawlett's cross.
At the other end, Nigel Hasselbaink jinked his way into the area and went down as Dons skipper Russell Anderson hung a leg out. Referee Steven McLean had a clear view, though, and booked the Dutchman for diving.
Midway through the first half, Dave Mackay drove a free-kick from the corner of the area towards Jamie Langfield's goal which the goalkeeper tipped over.
With regular goalkeeper Alan Mannus sidelined through injury, 41-year old player-coach Banks was in goal for the Saints. Wylde forced him into a full-stretch save with a flicked volley from Mark Reynolds' cross.
With the deadlock still to be broken the Dons replaced Hector, who had started well but faded as the game went on, with Cammy Smith at the interval.
Some of the home support were on their feet six minutes into the second period as Magennis got on the end of a McGinn cross at the near post, but the striker's header found only the side netting.
At the other end, the pace of Hasselbaink was troubling the Aberdeen defence. He found Murray Davidson with a cutback from the right, but the midfielder somehow blazed over the crossbar when finding the net seemed simpler.
The game was beginning to open up and twice in the space of a minute, Aberdeen should have opened the scoring.
First, Smith saw his powerful 20-yarder beaten away by Banks. The ball was worked back across the edge of the area, and Magennis then sent a low left-footed strike wide of the right-hand upright.
The Saints' first change saw May replace Steven Maclean in attack, but it was Aberdeen who would be next to threaten.
Clark Robertson's long ball dropped kindly for McGinn, who smashed a half-volley off the crossbar. Magennis was set to pounce on the rebound but was flagged offside.
That sparked a period of pressure for the home side, with Wylde denied by Tam Scobbie's last-gasp lunge. 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.
Both sides made changes after 76 minutes, Craig Murray replacing Shaughnessy and Liam Caddis taking the place of Hasselbaink.
Anderson had a late chance as his header was cleared off the line, but he was adjudged to have fouled Wright in any case.