The Windies, who lead the three-match series 1-0, dismissed the Indians for 359, a total that was made possible by Uday Kaul (64) who held the lower order together after the hosts began the day on 191 for three.
Juneja's unbeaten 178 ensured that India A ended the third day of their four-day fixture at 408 for 7, trailing New Zealand A's first innings total of 437 by just 29 runs.
Jagadeesh began the day at 126 and fell short of partners. None of the other Kerala batsman could score even a fifty as Akshat Kodoth was the next best batsman with a score of 32.