Goran Stevanovic's charges have found themselves embroiled in a battle to avoid the drop, after previously going on a nightmare run of 15 league games without a win.
But they boosted their top-flight survival hopes with a late flourish at the Qingdao Tiantai Stadium.
After a goalless first half, Qingdao looked to be heading for more disappointment when Tianjin stole ahead through Bare's strike in the 58th minute.
However, the visitors were ahead for less than 10 minutes as Australian forward Joel Griffiths levelled proceedings for the hosts.
Qingdao then took the lead eight minutes from time through a Bruno Meneghel penalty, before Zhu Shiyu gave them breathing space in the 87th minute.
And Griffiths then added his second of the game deep into injury-time to ensure Qingdao leapfrogged Changchun Yatai into 14th place.
Meanwhile on Friday, Liaoning Whowin moved up to seventh with a 1-0 triumph over Shanghai SIPG at the Shenyang Tiexi Stadium.
Argentine midfielder Pablo Brandan scored the only goal of the game with a penalty in the 34th minute.
The away side pushed for an equaliser, but Ma Lin's team held on for the three points.
