Striker Ciftci, who signed from Dundee United this week, came off the bench and won a free-kick late on, which he then laid off for Mackay-Steven to fire home from inside the box.
In Celtic’s final warm-up before their Champions League qualifier, played at St Mirren Park due to ongoing renovations at Celtic Park, Moyes’ Spanish side had a strong first half and were unlucky not to take the lead.
Craig Gordon was called into action after just three minutes, saving well from Yuri Berchiche, before Sergio Canales smashed a 25-yard drive against the post 10 minutes later.
Celtic’s best response was a Leigh Griffiths low drive that hit the woodwork five minutes after the restart after capitalising on slack play in the Sociedad defence.
Ciftci replaced Griffiths on 67 minutes to rapturous applause from Celtic fans, and his first involvement was to win a free-kick just on the edge of the box with his trickery.
After setting up Mackay-Steven to open the scoring, Ciftci had a chance of his own when he tried to chip Sociedad Geronimo Rulli but the ‘keeper managed to block.