The two sides are battling for the right to join PSV Eindhoven at Europe's top table and met in the first leg on Sunday.
AZ took an early lead when Simon Cziommer lobbed Maarten Stekelenburg.
Holland international Wesley Sneijder netted a fine solo effort on 13 minutes to level the scores, but Arveladze (pictured) netted from close range in the last minute to hand AZ the advantage.
An early goal from Anduele Prijor and header from Danko Lazovic on 78 minutes handed Vitesse Arnhem a 2-0 win at NEC Nijmegen and put them in pole position to claim a spot in the Intertoto Cup
Early goals from Luis Suarez and Yevgeny Levchenko handed Groningen a cushion over Utrecht and a late penalty from Gregoor van Dijk was not enough to deny the home side a spot in the Uefa Cup.
Utrecht will now face Vitesse for a spot in the Uefa Cup.
RBC Roosendaal and Excelsior played out a 1-1 draw in their promotion/relegation play-off, while VVV Venlo ran out 2-0 winners over RKC Waalwijk.
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Does anyone know if SAF was at the game? who played good of Ajax?