The narrow victory in front of 13,000 fans in the Croatian capital saw Zagreb maintain their 100 per cent home record, which was on the line in the final moments as the French side pushed hard to get something out of the match.
But thanks to the brilliance of goalkeeper Filip Ivic in the final moments, Zagreb managed to hold on and ensure they head into the winter break in a winning vein.
It was the third defeat of the season for PSG, who were a little lacklustre although their place in the last 16 already assured and they remain in second place in Group A, four points behind leaders Kiel.
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Zagreb are third, on eight points, one ahead of Naturhouse La Rioja and two ahead of HC Meshkov Brest with two places in the knock-out stage still up for grabs.
Zagreb started the stronger of the two sides as Paris struggled with their hosts more physical style of play.
Yet despite trailing from early on in the encounter, PSG never let Zagreb out of their sights. A Xavier Barachet goal after the half-time break even pulled the visitors level, although parity was brief and from that point on Zagreb did not lose their lead.
It could have been a different story if it were not for Ivic though, the keeper making a string of crucial saves to ensure his side registered their fourth victory of the season.
Heading into the winter break and with eight of the 10 group stage rounds played, the identities of 12 of the teams heading through to the last 16 are known.
Along with Group A's PSG and Kiel, FC Barcelona, KIF Kolding-Kobenhavn, SG Flensburg-Handewitt and Orlen Wisla Plock have confirmed their progress from Group B.
In Group C MKB-MVM Veszprem, HC Vardar, Rhein Neckar Löwen and Montpellier Agglomeration HB are through, while Vive Tauron Kielce and MOL-Pick Szeged have progressed from Group D.
The season kicks back into life on February 11 when defending champions Flensburg-Handewitt host MOGAZ HT.
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