The marquee striker beat Shanghai goalkeeper Yan Junling from the spot after Kosta Barbarouses appeared to be fouled outside the box, only for the referee to signal a penalty.
After starting promisingly and then surviving a surge from the visitors on Wednesday, Victory hit the front through shock starter Jai Ingham.
The 22-year-old winger - a January signing from NPL Victoria club Hume City - notched his first goal in professional football, bursting onto Oliver Bozanic's brilliant through-ball to score in the 31st minute.
Shanghai levelled the match six minutes into the second half, with Wu Lei tapping in Elkeson's teasing cross at the back post.
The Chinese Super League club had the better of the chances for the next quarter of an hour but it was Victory who struck the winner, with Berisha converting a 73rd-minute spot-kick.
In a frantic finale, Victory substitute Connor Pain and Shanghai playmaker Dario Conca both hit the post but the hosts held on for three points.
This article was originally published at: http://www.a-league.com.au/article/victory-stun-shanghai-sipg-in-acl-thriller/1sk8gajc3l3og1rjp0skpceruh.