The defender scored a late opener against Motherwell in October to send his team into the League Cup semi-finals and his early goal at Firhill proved enough to win this William Hill Scottish Cup fourth-round clash.
Aberdeen created a number of first-half chances before a tighter second period and they showed the resilience to bounce back from consecutive defeats by Hearts and Celtic to shut out a Thistle side that lacked a threat in the final third.
Aberdeen have scored seven goals without reply in two Scottish Premiership meetings with Thistle this season and they needed less than four minutes to add to their tally.
Barry Robson whipped in a swerving corner from the right and Considine rose unchallenged to head home from four yards.
The Dons, who were without injured winger Jonny Hayes, could have put the game out of sight in the first half against a side who had former Aberdeen midfielder Isaac Osbourne playing at right-back after Stephen O’Donnell and Jordan McMillan were ruled out through injury.
Peter Pawlett went down in the box after a shoulder charge from Mark Kerr but made little of it and soon won the ball back before unleashing a 30-yard volley that Scott Fox parried at full stretch.
Fox soon made an even better stop following good wing play from Gregg Wylde after Ryan Jack’s shot took a major deflection off a Thistle defender. The Thistle keeper was going the wrong way but readjusted his body to make a diving stop.
Thistle, who had Aaron Muirhead and Stuart Bannigan suspended, were making no inroads into the Aberdeen defence with their possession and a misplaced pass from James Craigen inside his own half sent Wylde bearing down on goal, but the former Rangers player shot high and wide.
Aberdeen had another good chance from a corner with five minutes remaining of the half but Calvin Zola headed just over from Niall McGinn’s inswinger.
Kallum Higginbotham soon had a half chance at the other end but dragged a shot wide from 25 yards as he broke in the left channel.
The second half saw few chances. Higginbotham looked busy for Thistle but could not find a killer pass and the Aberdeen defence coped well with some decent deliveries from Ross Forbes.
Wylde and Zola came off for Josh Magennis and Cammy Smith just after the hour mark while Thistle captain Sean Welsh made his comeback from injury when he replaced Kerr.
But the pattern of play did not change as Aberdeen remained firm when faced with spells of Thistle pressure.
McGinn came close several times on the break before Jamie Langfield made his first real save in the 79th minute when he beat away Higginbotham’s curling effort from 20 yards.
Jags boss Alan Archibald brought on Steven Lawless and John Baird but Thistle could not find the spark needed to fashion an equaliser and McGinn fired against the inside of the post in injury time following a good break by Jack.
Partick Thistle: Fox, Taylor-Sinclair, De la Vega, Balatoni, Osbourne, Forbes (Lawless 76), Kerr (Welsh 62), Higginbotham, Craigen, Elliot, Doolan (Baird 80). Subs not used: Gallacher, Mukendi, Wilson, Meechan.
Aberdeen: Langfield, Reynolds, Considine, Anderson, Hector, Jack, Wylde (Smith 61), Robson, Pawlett (Vernon 86), McGinn, Zola (Magennis 61). Subs not used: Shaughnessy, Low, Weaver, Murray.