There's a place that does general alterations, I'm sure they'd do a zip repair, on the 1st floor of Sihl City next to Coop.

Botique Selection is what you are looking for

Usterstrasse 3, Dübendorf

here's a list of seamstress studios in Zürich according the the yellow pages

http://yellow.local.ch/de/q/Zürich/Nähatelier.html

Accros from Globus (Lowenplatz) Next to the Valentino coiffeur there is one clothing repair. 

There is one close to Bahnhof SchmiedeWiedikon Birmerdorferstrasse if you walk away from the station (away from the city) it is after the chinese food store. 

There's one at Tramstop Englishviertelstrasse Tram 15. 

 I had to search 2, so I understand where your coming from hahaha

Cheers,