Fast bowler Duanne Olivier was the wrecker-in-chief as he claimed six wickets to trigger the India collapse after the hosts resumed at overnight 322 for four.
The former India captain said the leg spinner has the skills and has been given the chance to prove himself in the ongoing 'A' series against South Africa.
However, it was a toil for the India A bowlers on the final day as it took them 88.5 overs to get the final six wickets.
When stumps were taken due to bad light, the visitors were trailing by 239 runs after India A declared their first innings at 584 for eight.
Agarwal sent the bowlers on a leather hunt with an unbeaten 220 off 250 balls while Shaw punished them with a well-made 136 off 196 balls during a 277-run opening stand.
Leg-spinner Yuzvendra Chahal picked up one as India kept a tight leash on the South Africans, who opted to bat after winning the toss.
It is widely believed that Chahal is being kept match-ready as the selectors have named senior squad for only three Test matches in England.
Promising top-order batsman Shreyas Iyer will lead the India A team in the four-day games against the South Africans and the shift was made due to citing of heavy rains during the matches.
There is a school of thought that Ravindra Jadeja will be slowly eased out of the longer version if Chahal is able to show his skills in the four-day games.
The sole silver lining for India A was that Ajinkya Rahane and rookie Risabh Pant got to spend some valuable time in the middle ahead of the five-Test series against England.
England Lions tightened the screws on India A as they dismissed the visitors for 197 and were going strong at 159 for 4 in their second innings.
Shaw top-scored with 62 for India A at the County Ground, but others such as Test specialist Vijay, Mayank and skipper Nair failed to get going.
Having conceded a first-innings lead of 110 runs at The Cooper Associates County Ground, India 'A' eventually chased down a target of 321 with plenty to spare.
India A never looked back after losing the tri-series opener to Lions, beating the hosts and the West Indies A twice to lift the trophy.
Mayank Agarwal continued his dream run with yet another hundred as India A comfortably beat England Lions by 102 runs.
Mayank Agarwal smashed a breezy century as India A recorded a convincing seven-wicket victory over West Indies A.
Gurbani got his maiden call to the Indian A squad for the England tour following an impressive 2017-28 Ranji Trophy season in which he picked up 39 wickets for Vidarbha.
India A piled up a mammoth 458 for 4 to win the second warm-up game by a massive 281 runs ahead of their tri-nation one-day series starting June 22.
CoA chief Vinod Rai informed that Indian cricketers will leave for England in two batches in June.
India B are in the finals having defeated India A in the opening game of the tournament.
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