Joe Ledley, Adam Matthews, Charlie Mulgrew, Virgil van Dijk and Gary Hooper were all absent due to injury although captain Scott Brown managed 60 minutes as he continues his recovery from a groin injury.
Celtic had lost 6-2 to Union's Bundesliga 2 rivals Greuther Furth on Tuesday and they found themselves behind inside 11 minutes at a packed Stadion An der Alten Forsterei, where around 20,000 fans were marking the opening of the new main stand.
Midfielder Tomas Rogic lost the ball midway inside his own half and it was helped on to Simon Terodde, who unleashed a 20-yard volley that swerved past Fraser Forster into the roof of the net.
Forster appeared to be taken by surprise by the effort but he pulled off an impressive stop moments later before Celtic improved in the latter stages of the half with Mikael Lustig heading not far wide.
But some slack defending cost the Scottish champions 10 minutes after the restart with Celtic failing to react as a half-cleared corner was sent high back into their box for the unmarked Soren Brandy to stab home.
Union had a goal disallowed for offside before Australian youngster Jackson Irvine and Anthony Stokes got efforts on target, but Celtic conceded another soft goal three minutes from time.
The visitors, who also lost to Ukrainian side Sevastopol and Romanians Cluj on their tour of Germany, failed to pick up at a short corner and the ball was crossed for Damir Kreilach to rise above substitute Amido Balde and head home from close range.
Celtic will now be hoping to halt the losing run in their Champions League qualifier against Cliftonville in Belfast on Wednesday night.