The home side threatened first, but Mark Corcoran's outswinging cross was just too high for Garry Brady.
After eight minutes, a Scott Severin throw-in was held up by Darren Mackie and, after a mini-scramble, the ball broke to Considine who, from eight yards, sent a low drive beyond Chris Smith.
Severin sent a swerving shot whistling past Smith's right-hand post and Mackie outpaced Kirk Broadfoot only to run the ball out as the Dons went for a second.
Mackie and Steve Lovell were tearing the home defence apart at will and Smith denied both strikers when they were clean through within a minute of each other.
Eight minutes from the break, Barry Nicholson's corner was missed by Russell Anderson, but Considine met the ball from the edge of the penalty area and cracked a low drive in off a post.
Saints changed things around after the break and posed more of a threat, John Potter shooting just past and Corcoran thrusting into the box only to fire a tame shot at Jamie Langfield.
Broadfoot blasted over from six yards after Aberdeen failed to clear a Simon Lappin free-kick, but the visitors might have had a third when Lovell emulated Broadfoot after Kevin McGowne headed a clearance to him.
Seven minutes from time, Considine brought down Broadfoot, but Langfield leapt nimbly to his right to palm away Richard Brittain's powerfully-struck penalty.