With 18 players out injured or absent through other commitments the excuses were ready-made for the German, who had previously steered his adopted nation to four straight losses.
But they were not necessary as McFadden's 76th-minute strike made sure a performance that had seen plenty of earlier chances go a begging was not wasted in the end.
Vogts handed the captaincy to 20-year-old Darren Fletcher, who became the youngest Scot to lead out his country since 1886.
The Manchester United man was all action in an attacking midfield role, spraying passes in all directions when he was not taking on men himself.
Debutant Nigel Quashie, the former England B international who re-qualifies through a Glaswegian grandfather, was there alongside him in a starting line-up that saw two other debutants Quashie's Portsmouth colleague Richard Hughes at left-back and David McNamee of Livingston at right-back.
The Scots will end a topsy-turvy season in an Edinburgh friendly with Trinidad and Tobago on Sunday.
: Kaalma, Allas, Stepanov, Jaager, Klavan, Rahn, Reim, Viikmae, Terehhov, Oper, Lindpere (Kink 75).
: Gallacher, McNamee, Pressley (Webster 46), Mackay, Hughes, Gary Caldwell, Holt, Quashie, Fletcher, McFadden (Kerr 89), Kenny Miller (Crawford 79).
: Tonny Poulsen (Denmark).
: Germany 7 Malta 0.