For the hosts, leg-spinner Devendra Bishoo, who has struggled in the series with just a one wicket in the previous two matches, returned to form by claiming three for 40 and effecting a brilliant run out at the Beausejour Cricket Stadium.
The 25-year-old was well-supported by seamer Jonathan Carter who picked up three for 67 giving the Windies a slight edge in a series that is tied 1-1 at the moment.
Right-handed Saxena top-scored for the Indians with a breezy 61 while captain Cheteshwar Pujara got 33 and Ajinkya Rahane and Manoj Tiwary made 32 apiece.
In reply, West Indies A were 34 without loss, with Test opener Kieran Powell unbeaten on 16 and out-of-favour senior team batsman Kraigg Brathwaite on 13. It was once again a shambolic performance by India`s top-half batsmen, who have failed consistently in the series.
West Indies A reduced the visitors to 32 for two early on in the first innings after speedster Delorn Johnson sent back Abhinav Mukund (10), caught at second slip by Carter, and Rohit Sharma (12) who was clean bowled.
Rahane and Pujara added 46 runs for the third wicket, before the former fell just before lunch, caught behind off left-arm spinner Veerasammy Permaul.
Pujara was run out by Bishoo, who sent a return from deep cover to leave the batsman short of his ground as he dashed for a third run.
India A slipped to 116 for five in the post-lunch session before a sequence of small partnerships helped them go past the 200-run mark.
Tiwary and wicketkeeper Wriddhiman Saha (27) put on 30 for the sixth wicket before Saha and Saxena added a further 33 for the seventh wicket. Saxena smashed 10 fours off just 59 balls. He was Bishoo`s second wicket, caught by Brathwaite at mid-wicket. Bishoo`s third wicket came when he bowled Parvinder Awana for a nought to wrap up the innings.