Leverkusen had started with four straight competitive wins - including two in the Europa League qualifiers and one in the German Cup - but never looked like continuing their run after teenager Patrick Herrmann netted twice to help Moenchengladbach go 3-1 up at half-time.
The score was 5-2 by the time an ineffective Ballack, left out of Germany's squad for next month's Euro 2012 qualifiers, was taken off in the 63rd minute, having played the full 90 minutes in last week's 2-0 win at Borussia Dortmund.
Ballack, who missed the World Cup with an ankle injury, was signed from Chelsea in the close season.
Dortmund won 3-1 at VfB Stuttgart in Sunday's other game to complete a weekend which saw champions Bayern Munich beaten 2-0 at promoted Kaiserslautern and former England manager Steve McClaren's VfL Wolfsburg lose 4-3 at home to Mainz 05, having led 3-0.
Hoffenheim, Kaiserslautern, Hamburg SV, Mainz and Hanover 96 have all won their first two games.
"Defensively this was a catastrophe," said Leverkusen goalkeeper Rene Adler. "You cannot allow six goals at home... this will bring us back to reality."
WILDEST DREAMS
Stunned Moenchengladbach coach Michael Frontzek said: "This was a perfect away game for us... we couldn't have imagined this in our wildest dreams."
Moenchengladbach, who have four points from two games, went ahead in the 20th minute when Mohammadou Idrissou took the ball from Arturo Vidal and sent over a low cross which 19-year-old Herrmann fired into the roof of the net from close range.
Leverkusen, who have three points, equalised four minutes later when Switzerland forward Eren Derdiyok outjumped the defence to head home Gonzalo Castro's cross.
Stefan Kiessling headed against the bar soon after for Leverkusen but two quick goals before half-time put the visitors in charge.
In the 40th minute Dutchman Roel Brouwers tapped in after Adler failed to hold a long-range shot by Thorben Marx and five minutes later Herrmann rifled in a 25-metre shot.
It got worse for Leverkusen when Venezuela midfielder Juan Arango curled a superb 30-metre free-kick into the top corner in the 56th minute to make it 4-1.
Chile midfielder Vidal won and converted a penalty for Leverkusen two minutes later but, another two minutes on, Cameroon's Idrissou added Moenchengladbach's fifth from close range after Arango's shot was parried by Adler.
Marco Reus fired the sixth in the 69th minute before Kiessling, the second-highest Bundesliga scorer last season with 21 goals, pulled one back a minute later.
Dortmund raced into a 3-0 half-time lead thanks to a Khalid Boulahrouz own goal, a right-foot shot from Paraguay forward Lucas Barrios and a Mario Goetze header. Germany forward Cacau pulled one back for Stuttgart after half-time.
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