Around 10,000 Serbia fans, mostly expatriates living in Austria, attended the match and trouble erupted in the second half when they threw burning flares, bottles and missiles on to the pitch.
Several of them then invaded the turf and had to be dragged away by security before Vidic, deputising as skipper for Dejan Stankovic, stepped in to urge calm as the match officials and New Zealand's players were getting ready to walk off.
The match was held up for several minutes before restarting.
The ugly scenes compounded a miserable afternoon for Serbia, whose experimental line-up was bereft of pace and ideas.
New Zealand, in contrast, stuck to their trademark hardworking approach and it paid dividends when Shane Smeltz scored the only goal in the 22nd minute.
The striker took a long ball into his stride and easily beat right back Antonio Rukavina, one of Serbia's second-choice starters who disappointed, before he steered a low shot into the bottom right corner.
The Kiwis came close to doubling their lead only three minutes later, when Rory Fallon saw a thunderous shot parried after he was set up by Smeltz.
Serbia improved after the break as Zoran Tosic made several darting runs on the left wing but his good performance was the only positive that coach Radomir Antic can take from an afternoon he will quickly want to forget.
The Serbians play Poland in Kufstein on Wednesday in the other match of their build-up in Austria and take on Cameroon in Belgrade on June 5 in their final warm-up before they depart for the month-long World Cup finals in South Africa.
Serbia are in Group D along with Germany, Australia and Ghana while New Zealand contest Group F with Italy, Paraguay and Slovakia.
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