Yu Kobayashi's low drive put hosts Kawasaki in front with eight minutes on the clock, but goals from Park Yong-woo and Junior Negrao saw Ulsan edge towards the win required to guarantee their progress.
But Kei Chinen's close range 82nd minute finish earned Kawasaki a share of the points and delayed Ulsan's qualification for the next phase by at least two weeks.
Ulsan now have eight points from four games in group H and are three points clear of SIPG, who were held to a 2-2 draw by Sydney FC at Shanghai Stadium.
Brandon O'Neill gave Sydney the lead with the most delicate of finishes only for substitute Elkeson to level with a header two minutes after coming on at the start of the second half.
Wang Shenchao then put Vitor Pereira's side in front at the end of a sweeping move in the 59th minute, only for Adam Le Fondre to equalise for Sydney three minutes later.
"We were disappointed to get the draw tonight, we were probably good value to get the win," said Le Fondre.
"We were pushing all the way, and we looked to be the team in the ascendancy come the end of the game, and we're really disappointed the full time whistle went."
Japan's Sanfrecce Hiroshima notched up their third victory in a row to move into pole position in group F as the current J-League leaders defeated their South Korean hosts Daegu FC 1-0 courtesy of a Hayako Araki goal.
That win sees Hiroshima go two points clear of two-time champions Guangzhou Evergrande, who were held to a 1-1 draw in Australia by Melbourne Victory.
China international midfielder Huang Bowen gave Fabio Cannavaro's side the lead in the 24th minute and just two minutes later Jai Ingham levelled for Melbourne, although it was not enough to keep his club's slim hopes of a place in the next phase alive.
Evergrande are now second in group F on seven points, one point ahead of Daegu FC, while Melbourne have a solitary point and cannot finish in the top two positions due to their inferior head-to-head record against Guangzhou.
In the west of the continent, Xavi Hernandez scored his third goal in two games when he opened the scoring for Al Sadd in their 2-1 win over Uzbekistan's Pakhtakor as the Qatari club moved into top spot in group D.
Al Sadd lead by a point from Saudi Arabia's Al Ahli, who had an Omar Al Soma brace to thank for their 2-1 win over last year's beaten finalists Persepolis from Iran.
Al Wahda from the United Arab Emirates, meanwhile, lead group B by two points from two-time champions Al Ittihad of Saudi Arabia after Brazilian striker Leonardo hit the back of the net four times in their 4-3 win over Qatar's Al Rayyan.
Al Ittihad were held to a 1-1 draw by Lokomotiv Tashkent from Uzbekistan.
(Reporting by Michael Church; Editing by Hugh Lawson) ((Michael@asiansportsmedia.com, +852 9023 4874))