After an entertaining, open first half which remained scoreless only due to the excellence of Peter Kjaer and his opposite number in the home goal, the Dons broke the deadlock 7 minutes into the second period.
Skipper Darren Young notched his second goal in as many games driving home a well placed 18 yard shot after a neat lay off by Leon Mike.
The Dons looked set to hang on for a fine victory but they were denied eight minutes from time as Knarvik rifled home a deep cross from the left which Phil McGuire struggled to clear.
Aberdeen used only two substitutes - Derek Young being replaced by Scott Michie after sixty five minutes while Bob Duncan came on for Kevin McNaughton a minute from time.