The Reds needed a superb save from goalkeeper Eugene Galekovic just before the hour mark to ensure they at least took a point against the struggling Jets, who saw marquee signing Emile Heskey limp out at half-time.
Adelaide's slip means leaders Central Coast Mariners could move four points clear when they travel to in-form Western Sydney Wanderers on Sunday.
Wellington Phoenix's Melbourne misery continued as they suffered a 2-0 defeat at AAMI Park.
The Phoenix have never won an A-League match in the Victorian capital and were overcome by their former midfielder Marco Rojas, who scored one goal and assisted Marcos Flores for the other.
Victory had to wait until the 36th minute for their first genuine chance.
Diogo Ferreira began a break that ended with a Rojas ball to Archie Thompson in the six yard box, but the Phoenix defence did enough to put the veteran striker off.
Melbourne grabbed the lead three minutes before half-time when Flores found himself on the end of a Rojas cross from the left that somehow travelled through a busy Phoenix area, poking home past goalkeeper Mark Paston at his near post.
It took just six minutes of the second half for the scoreline to become 2-0.
Rojas had shown a knack for the spectacular in previous weeks, but also demonstrated he could do the simple things when he tapped home from close range.
Rojas created the chance by feeding Adrian Leijer, and - though the Victory captain's shot was weak - it still did enough to beat Paston before rebounding off the post into the New Zealand international's path.
Perth Glory twice squandered the lead against Sydney FC, a result which did little for either side.
Glory went ahead through Shane Smeltz six minutes before the break only for Jason Culina to equalise midway through the second half.
Smeltz restored the lead 10 minutes from time but they were ahead for only two minutes before Sebastian Ryall scored the visitors' second leveller of the game.
The result leaves Glory four points behind Western Sydney Wanderers while Sydney remain bottom, a point behind Melbourne Heart.