Chasing 231, India lost its opening two wickets with just 58 runs on the board as Sachin Tendulkar (41) and Manoj Prabhakar (9) were sent back to the pavilion.
It was then, that Azharuddin and Navjot Singh Sidhu got together at the crease and formed a 175-run stand to take India over the line by eight wickets.
Azharuddin and Sidhu remained unbeaten on 90 and 84 respectively.
While bowling, Ventakesh Prasad and Anil Kumble scalped two wickets each to reduce Sri Lanka to 230/7 in the allotted fifty overs.
WATCH: India vs Sri Lanka 1995 Asia cup highlights here
The 1995 Asia Cup was played in a round-robin tournament where each team played the other once, and the top two teams qualified for the finals.
In the tournament, India, Pakistan, Sri Lanka and Bangladesh participated.
India, Pakistan and Sri Lanka all had four points at the end of the round-robin stage, but India and Sri Lanka qualified for the final on the basis of better run-rates.
So far, 14 editions of Asia Cup have been played and India has managed to win the tournament seven times.
In the latest edition in 2018, India went on to win the tournament after defeating Bangladesh in the finals.
Sri Lanka has won the Asia Cup five times while Pakistan has managed to achieve the feat two times.
Asia Cup is scheduled to be played later this year as well, but right now, the fate of the competition hangs in the balance due to the ongoing coronavirus pandemic.
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