Chennai drew first blood in the 71st minute through Spanish midfielder Sandro's free-kick and concluded their game with another goal from substitute Vijay N during the stoppage time.
Chennai, as expected, started the game on an attacking note, in their effort to bag full points.
After a barren first half, Chennai City kick-started their second half, attacking at regular intervals but were unable to find the back of the net.
Credit for a valiant Arrows show should also go to their goalkeeper Samik Mitra, who stood tall under bar, denying Chennai City FC, any opportunity to capitalise on errors.
As the game entered the final quarter, Chennai City visibly grew frustrated with their inability to break into the Arrows defensive line.
Their efforts finally paid dividends when a risky tackle in the 71st minute from Indian Arrows from the edge of the box, led to a yellow card for Suresh Singh, gifting the visitors a free kick from a dangerous spot.
Chennai's Spanish midfielder Sandro broke the deadlock with perfectly taken free-kick. The tally was rounded off by Vijay, who found the back of the net with a rebound in the 91st minute of the match.
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