Ulsan were last denied victory on the continental stage in April 2012 against Brisbane Roar, with the South Koreans going on to clinch the title that year.
And when Rafinha put the hosts ahead from the penalty spot just before the hour mark on Wednesday, Ulsan looked set to extend their streak to 12 matches and make it nine points from their opening three games on their return to the competition this season.
However, Yang headed home Sun Jihai's delivery after 87 minutes as Renhe snatched a point.
That result allowed Western Sydney Wanderers to close the gap between themselves and the leaders to a point at the top of Group H.
Labinot Haliti scored the only goal of the game three minutes in against Kawasaki Frontale, much to the delight of coach Tony Popovic.
"It is a fantastic achievement and a fantastic result and it gives us a chance (of reaching the knockout stage) now," Popovic said.
Tsukasa Shiotani and Yojiro Takahagi helped J.League champions Sanfrecce Hiroshima to a first win in nine Champions League matches against Seoul.
The sides now sit level on points in Group F after Sanfrecce's 2-1 victory while Chinese outfit Beijing Guoan are top after their 2-1 win over Central Coast Mariners.
Shao Jiayi and Peter Utaka were on target for the hosts either side of half-time, while they survived a late scare when Nick Fitzgerald pulled a goal back for the Australians from the spot four minutes from time.
Bunyodkor snatched a point at home against Iranians Foolad in Group B thanks to Vokhid Shodiev's injury-time equaliser while El Jaish and Al Fateh also ended level - both sides failing to score at the Prince Abdullah bin Jalawi Stadium.
Al Sadd remain top of Group D after Talal Al Bloushi and Nadir Belhadj cancelled out Thiago Neves' brace to ensure a 2-2 draw against Al Hilal and Sepahan were beaten 2-1 by Al Ahli.
Ismaeel Al Hammadi scored the crucial goal five minutes into injury time - moving the visitors level on points with leaders Al Sadd.
