A 70th-minute equaliser from Joffre Guerron, which cancelled out Junzhe Zhao's 55th-opener for Liaoning, gave Beijing hope of snatching all three points but they could not find a winner in the final 20 minutes.
The result leaves Beijing three points ahead of fourth-placed Guizhou Renhe but that gap could be erased on Sunday when Renhe take on Shanghai Shenhua.
Beijing's draw also ended any slim hopes they might have had of snatching second place off of Shandong Luneng, who are 11 points clear heading into Sunday's top-of-the-table clash with Guangzhou Evergrande with just three rounds to come afterwards.
Beijing are slight favourites to claim third spot for a second successive season, but as well as Renhe, both Guangzhou R&F and in-form Tianjin Teda still have an outside chance of a top-three finish.
Guangzhou are eight points behind Beijing after beating Changchun Yatai 1-0, experienced Nigeria striker Ayegbeni Yakubu netting a 56th-minute winner, while Tianjin Teda are three points further back but with a game in hand after downing Dalian Aerbin 2-0.
Yang Cao opened the scoring in the 42nd minute and Carmelo Valencia added a second 13 minutes from time as Tianjin recorded a fifth successive win.
At the other end of the table, rock-bottom Wuhan Zall's relegation was confirmed after they could only draw 0-0 at second-bottom Qingdao Zhongneng, who are still fighting for survival and now are just a point behind Changchun and safety.
In Saturday's other games, a second-minute Sun Kai own goal gave Shanghai Shenxin a derby win over Shanghai SIPG, while Hangzhou Greentown drew 1-1 at home to Jiangsu Shuntian, Cristian Danalache netting an 88th-minute equaliser for the visitors after Hangzhou had led through a 15th-minute Davy Angan goal.