Anthony Modeste scored with a minute remaining of the game at a sold-out Mong Kok Stadium. The Frenchman's winning header means Tianjin cannot finish outside the top two places in Group E.
"I said to my players three days ago that this game would be demanding and it was, but we have qualified and we are ready to go into the next phase," said Tianjin head coach Paulo Sousa.
"It's historic for us to qualify for this phase, so to go to the next round it is a top performance from my players."
Tianjin are second in the group behind two-time champions Jeonbuk Motors who are also through to the next round after a 2-0 win over Kashiwa Reysol in Japan.
Veteran striker Lee Dong-gook claimed a record-extending 36th career goal in the competition after Ricardo Lopes had put the South Koreans ahead.
Tianjin became the second Chinese Super League side to advance to the last-16 after Shanghai SIPG, who guaranteed themselves first place in Group F with a 1-1 draw against Japanese champions Kawasaki Frontale.
Elkeson put SIPG in front in the 68th minute after Hulk had missed an earlier penalty but Kei Chinen levelled for already-eliminated Frontale six minutes later.
Shanghai are joined in the next round by South Korea's Ulsan Hyundai, who thrashed Australia's Melbourne Victory 6-2 to end the hopes of Kevin Muscat's team.
Junior Negrao and Mislav Orsic both scored twice to extend Melbourne's run of never having won a game away from home in the Asian Champions League.
In the west of the continent, Al Jazira claimed a 3-2 win over Qatar's Al Gharafa to book their place in the next round from Group A. They will be joined by Saudi Arabia's Al Ahli, who defeated Tractorsazi from Iran 2-0.
Qatar's Al Duhail maintained their perfect record with a 1-0 victory over Iran's Zobahan in Group B, while the battle for second is set to go down to the wire.
Lokomotiv from Uzbekistan thrashed Al Wahda of the United Arab Emirates 4-1 ensuring the club from Tashkent can advance to the knockout rounds with a two-goal win when they host Zobahan in two weeks' time.
(Reporting by Michael Church, Editing by Christian Radnedge)
