Set to score a challenging 301 in 50 overs for victory at a high asking rate of 6.02, the visitors rode on emphatic batting displays by skipper Russel Arnold (96 not out; 99b, 8x4, 1x6) and opener Samana Jayantha (92; 98 b, 11x4, 2x6) to reach the target losing only three wickets and with two overs to spare at the Eden Gardens.
Jayantha and Man of the Match Arnold put on 126 runs the third wicket to take the game away from the Indians after the tourists lost opener Kalavitigoda (18) and Jehan Mubarrak (25) to be in a spot of bother at 76 for two.
Jayantha returned to the pavilion eight short of his hundred, caught at deep mid-wicket by Sairaj Bahutule of Dinesh Mongia with the score reading 202. Arnold and his deputy Naveed Nawaz (57 not out; 44b, 4x4, 3x6) then stitched together a rollicking 99 run unbroken stand in only 56 minutes to take Sri Lanka 'A' to 301 for three in 48 overs.
However, both Jayantha and Arnold got 'lives' as they were dropped by the butter-fingered Indian fielders.
Jayantha, who moved from 47 to 53 with a straight field six of Bahutule, was dropped by Munaf Patel at backward square-leg with his personal score standing at 58. Jayantha tried to pull offie Sarandeep and only succeeded in getting a top edge, and the ball ballooned to Patel, who failed to latch on to the ball.
Arnold, on the other hand, survived a caught behind chance when Ratra failed to glove an easy catch. The Lankan skipper was then on two, and the unlucky bowler was Sarandeep.
Nawaz brought the end in style hitting Bangar out of the ground to level the score, before getting the winning run with a single in the last ball of the over.
Earlier, India 'A' scored 300 for eight, with Gambhir cracking a masterly 113 (125 b, 191m, 11x4, 1x6) and adding 159 runs for the second wicket with Mohammad Kaif (71; 124 m, 4x4) after skipper Hemang Badani won the toss and elected to bat.
The two came together after Sanjay Bangar (21) departed in the eighth over and took full advantage of wayward bowling by the Sri Lankans to execute a flurry of shots all round the wicket as India A reached 223 for 1 in the 39th over, looking well placed for a score of around 350.
Left-arm spinner Ranga Herath finally broke the stand when Kaif tried to pull him, but failed to control the shot, and S Jayantha brought off a fine catch at deep mid-wicket.
Gambhir, who looked in complete command, except one or two minor blemishes, completed his hundred soon after with a single, but then wickets started falling at regular intervals, as India 'A' batsmen went out to irresponsible shots. Yuvraj Singh (6), Badani (18), Bahutule (1), Ajay Ratra (1) departed cheaply, while Sarandeep (3) was run out.
At the end, Dinesh Mongia (23; 18b, 1x4,1x6) and Amit Bhandari (3) remained unconquered in the middle. A highlight of the morning was the erratic bowling of pacer Nuwan Zoysa who conceded as many as 38 runs in his first two overs, including 13 no balls and five wides.
However, the pick of the Lankan bowlers was Herath (1/45) who kept a good line and length.
Keen battle between arch rivals on the cards