Ghanian Daniel Addo (11th minute) and Syrian Khaled Alsaleh (64th) scored for the visitors, while the Arrows produced a spirited performance but failed to post any goals.
In the first half, Gokulam Kerala FC were the more attacking and even looked more in control even though possession was split equally.
The initial enterprise was shown by the Indian Arrows. In the 8th minute, the self-driven and pacy Aniket Jadhav first cut in from the left to play the ball to Abhishek Halder near the top of the box, but his feeble left footer lacked direction.
Then almost against the run of play, Kerala's Ghanian centre-back, Daniel Addo jumped high above everyone, off a Rohit Mirza corner from the left flank in the 11th minute, to drill a header into the Arrows net.
More From This Section
The Arrows defence could certainly have been more alert and proactive in marking Addo. The Arrows were clearly rattled and frustrated by the goal as Aniket earned the game's first yellow card in the 30th minute for his incessant aggression.
His attempt to break in was thwarted illegally by Anwar Ali, just outside the box. Khaled fired in a left-footer, but it rebounded off the goalline milee.
Then in the 37th minute, Abhishek Halder lost the ball inside his own half and Usman Ashik broke free into the Arrows box from the left.
His diagonal left-footer beat Dheeraj but rolled past the far post. Just at the stroke of the lemon-break, Gokulam got another chance when a lovely through ball from Usman found Rohit clear in the box with just the goalkeeper to beat. But Dheeraj, rushed out to clear just in time.
In the 58th minute, from one of those free-kicks from about 30-yards away, Sanjeev Stalin curled a vicious right- footer which beat the Gokulam keeper Bilal all ends up but struck the upright, in what turned out to be the Arrows best chance of the game.
Stalin's overenthusiasm post the free-kick though cost his team a second goal. He picked up a needless yellow card on the right flank with a reckless tackle on Santu Singh.
Stung by the reverse, Arrows tried their best to come back into the game and Usman was replaced by Syed Shoaib Ahmed in the 75th minute by Gokulam coach Bino George to ensure more muscle in the defensive midfield.
The Arrows coach Matos, made his last throw of the dice with a double substitution in the 86th and 87th minute. Abhijit Sarkar came in for Jadhav and Boris Thanjam was replaced by K. Meetei.
But in spite of the fact that most of the play was happening in the Gokulam half, the spirited Arrows side could not find a consolation goal.
Midfield spearhead Jaekson Singh made a comeback into the starting eleven and so did Aniket, the striker who struck twice in the Arrows opening game win against Chennai City FC.
Gokulam move from ninth to the seventh position on the points table with this win while the Arrows slipped to ninth place.