Strachan had shrugged aside talk about his sacking after a wretched start saw Celtic crash out of Europe but the little man's recovery now sees Rangers trailing in his wake in the Scottish Premier League after goals by Maciej Zurawski and Stilian Petrov marked the poignant 20th anniversary of Stein's death.
Celtic had chosen this day to celebrate the life of the man whose indelible imprint shaped this club. This anniversary - the legendary manager suffered a heart attack as his Scotland team secured a play-off place for the 1986 World Cup finals by drawing with Wales in Cardiff - was fitting, given that one of his players that night, Strachan, is now his successor.
It was Stein's status as a national icon that saw the Aberdeen fans join in the Italian-style tribute of a minute's applause, which rose to a deafening din. Out on the pitch were Stein's most famous team, the Lisbon Lions, with the European Cup that they won in 1967.
Strachan has had a difficult initiation but Celtic's recovery has echoed that of Zurawski. The Pole broke his duck a fortnight ago with a double at Dunfermline and continued in the same vein with two in Poland's subsequent World Cup fixtures.
Zurawski struck again 13 minutes into this encounter. John Hartson chested down Bobo Baldé's pass to Zurawski, and then played a one-two with his partner, to allow the Pole to race 40 yards before thrashing a shot high past the goalkeeper, Ryan Esson, from just inside the box.
Aberdeen simply could not make any impact. Celtic might have doubled their lead just before the interval as Petrov's pace saw him scamper clear before delivering a cross that Esson had to snatch off Hartson's head.
Celtic were unrelenting in the second half, with Petrov and Alan Thompson both going close, one with a volley the other with a header.
The comfort zone Celtic craved came on the hour with a sublime goal. Hartson rose to flick into the path of Zurawski who thought about going for goal but then held the ball up to wait for support, rolling a cutback into Petrov, who feinted twice to shoot before drilling an angled right-foot finish past Esson.
Strachan then brought on his tyros, Craig Beattie and Shaun Maloney, who posed further problems for Aberdeen before Jimmy Calderwood's side could escape to the dressing room.