The result was slightly cruel on Vietnam champions Song Lam, who dominated for much of the game but ultimately failed to apply the finishing touches to a number of well-worked openings.
And they were made to pay for their profligacy in the 51st minute when Malaysia international Abdul Manaf received the ball outside the box and beat Song Lam goalkeeper Tran Nguyen Manh with Terengganu's only effort of the game.
The hosts then piled on the pressure but failed to find an equaliser as their opponents defended resolutely, leaving Song Lam coach Nguyen Huu Thang lamenting his side's profligacy.
In Group F's other encounter, Tampines Rovers were beaten 3-1 by Hong Kong champions Kitchee at the Tseung Kwan O Sports Ground.
Liang Zicheng opened the scoring for the hosts after just three minutes, before Jamil Ali nodded home an equaliser midway through the first half.
However, further strikes from Liang and Jordi Tarres sealed all three points for Kitchee.
In Group B, Fatai Adisa Abao struck in first-half injury-time to help Al Orouba to a 1-0 win over East Bengal, while Arbil and Kazma played out a 1-1 draw.
Group A's action saw Al Qadsia cruise to a 2-0 win over Al Suwaiq courtesy of goals from Nawaf Al Mutairi and Omar Al Soma, while Al Faisaly were held to a 1-1 draw at home by Al Ittihad.
A brace from Rony Azar canceled out Mohamed Boqshan's 40th-minute strike to hand Safa a 2-1 win over Al Tilal in Group E's only game of the night.
Tuesday's AFC Cup Results
Al Qadsia 2-0 Al Suwaiq
Al Faisaly 1-1 Al Ittihad
East Bengal 0-1 Al Orouba
Arbil 1-1 Kazma
Al Tilal 1-2 Safa
Song Lam Nghe An 0-1 Terengganu