The former Anderletcht winger opened the scoring by the sixth minute after smashing Bai Yuefeng’s assist past goalkeeper Yan Junling.
Acheampong came close to doubling Teda's lead by the 49th minute but was ruled offside, while former Chelsea star Oscar fired wide two minutes later after connecting a cross from countryman Hulk.
Wenjun Lue brought the hosts level with a fine finish after a poor defending from Teda.
Shanghai came close on several occasions in pursuit of the match-winner, but the visitors eventually halted their six-game winning streak.
Acheampong was substituted by Yang Wanshun on the 90th minute.
In other related story, Ghana striker Richmond Boakye Yiadom played full throttle as Jiangsu Suning FC thrashed Shanghai Shenhua 5-1 to move to fourth position on the log.