It was another dominant performance from India as they continued their good run at home to record their 10th straight Test series win on home soil.
After scoring 367 runs in their first innings in reply to the West Indies' 311, India bowled out the visitors for 127 runs in the second innings on Sunday, setting themselves a 72-run target.
Ambris and Holder (19) delayed the inevitable after tea, adding 38 for the seventh wicket to keep India wicket-less for almost 40 minutes.
The incident occurred after West Indies opener Kieran Powell had been given out on the third and final day of the second Test. Powell fell to a low catch in the slips by Ajinkya Rahane, and the third umpire ruled that Rahane had caught the ball cleanly after watching numerous replays.
Ravindra Jadeja ended their stand, getting Holder caught behind for 19 and then trapping Ambris lbw.
The right-armer, who had figures of 6/88 in the first innings, bagged four wickets in the second innings conceding 45 runs and was also adjudged the "Man of the Match".
West Indies batsman Roston Chase heading off after he was bowled by Umesh Yadav. In the case of Shaw, the team management is keen to see how the youngster fares when given the opportunity even in the white-ball cricket. The Australian, who will turn 50 on Thursday, had announced he would quit his position once West Indies completed their tours of India and Bangladesh, and move to England to take charge of Middlesex.
On Sunday, India resumed the proceedings at 308/4 and lost five wickets in quick succession before Ravichandran Ashwin (35) and Shardul Thakur (4 not out) added 28 runs for the last wicket.