McGinn, now playing for Aston Villa in the English Premier League after helping them to promotion from the Championship via the play-offs, reacted quickest after Russian goalkeeper Guilherme Marinato spilled Ryan Fraser's cross under pressure from Oli McBurnie.
The 24-year-old won his 16th cap as he lined up at Hampden against Stanislav Cherchesov's side, with the Scots needing a win to keep their Euro 2020 hopes alive.
However, despite the strong start, Scotland were undone by a slick Russian side who equalised through Artem Dzyuba five minutes before half time before a Stephen O'Donnell own goal on the hour mark completed the come-from-behind win.