Dons right-back Ryan Jack was shown a straight red card for a wild lunge on Rangers transfer target Murray Davidson in the game's major talking point after 65 minutes.
Aberdeen had enjoyed the better possession and chances prior to the sending-off, but were unable to find a way past Peter Enckelman in the Saints goal.
Defender Youl Mawene and midfielder Isaac Osbourne both made their competitive debuts for Aberdeen.
With Jamie Langfield still recovering from a brain seizure, Colombian David Gonzalez started in goal for the Dons.
Richard Foster, back at Pittodrie following a season-long loan spell at Rangers, skippered the Dons with last season's top-scorer Scott Vernon and Darren Mackie leading the attack.
Former Celtic striker Cillian Sheridan started for St Johnstone following his loan move from Bulgarian outfit CSKA Sofia.
New signings Frazer Wright, Callum Davidson and David Robertson were also named in the Saints' starting XI.
Aberdeen made a confident start to the match but almost went behind after six minutes when Mawene failed to deal with Sheridan's inswinging cross, but Robertson was unable to turn the ball past Gonzalez.
Aberdeen captain Foster went close after 10 minutes when his dipping free-kick from 30 yards drifted just wide of Enckelman's post.
The home side's encouraging start continued when Foster went even closer three minutes later when his powerful drive from the edge of the area was palmed away for a fruitless corner by the Finnish stopper.
As the half progressed, the Dons continued to dominate proceedings with only some desperate defending from the Saints keeping the scores level.
Youngster Fraser Fyvie received the game's first yellow card after 36 minutes for a late sliding challenge on Robertson.
The Saints almost opened the scoring just before the break when Dave MacKay rose highest to nod Liam Craig's deep corner goalwards, but Gonzalez managed to gather the ball.
St Johnstone made an attacking change at the break by bringing an additional striker on in Markus Haber at the expense of midfielder Craig.
The visitors looked revitalised after the switch and could have made the breakthrough when Chris Millar released Haber, but Andrew Considine managed to block the striker's low shot.
The game ensued at a frenetic pace as the Dons raced up the other end with Fyvie sending Mackie through on goal, but the Dons attacker drove the ball straight at Enckelman.
St Johnstone survived another scare when a cross from Fyvie was terribly misjudged by Enckelman, who was struggling to deal with the swirling wind, and bounced back off the upright to safety.
Aberdeen were reduced to 10 men after 65 minutes when Jack was shown a straight red card for a rash lunge on Davidson.
Icelandic international Kari Arnason made his first Aberdeen appearance when he replaced the tiring Peter Pawlett three minutes later.
With less than 15 minutes remaining, the Saints introduced Kevin Moon and Stevie May for Sheridan and Robertson.
Josh Magennis, who had replaced the ineffectual Vernon, surged past two Saints defenders but the Northern Irishman dragged his eventual effort wide of the target.
Despite their numerical disadvantage, it was Aberdeen who finished the stronger but the visitors held on for a hard-fought draw.