Resuming the day's play on 234-5, Ashwin made 118 and Saha added 104 before India was bowled out in the second session
West Indies ripped through the India tail to bowl out the visitors for 353 runs on day two of the third test in St Lucia on Wednesday.
After Ravichandran Ashwin (118) and Wriddhiman Saha (104) added 213 runs in a stellar sixth-wicket stand, the final five Indian wickets tumbled for only 14 runs at the Darren Sammy Stadium in Gros Islet.
Ashwin and Saha made history by becoming the first India number six and number seven batsmen to score a century in the same innings. It was also Saha's first test century.
They came together at 126/5, but departed having guided India into a decent, if not quite unbeatable position.
Ashin brought up his century, his second in three knocks this series with a six over mid-wicket from the bowling of off-spinner Roston Chase.
But the West Indies will take heart from the way they quickly wrapped up the tail.
Fast bowlers Miguel Cummins and Alzarri Joseph both took three wickets, with fellow paceman Shannon Gabriel and spinner Chase claiming two.
Apart from Ashwin and Saha, only two other India batsmen reached double figures, opener Lokesh Rahul (50) and number four Ajinkya Rahane (35).
India lead the four-test series 1-0 after winning the opener at North Sound on Antigua and drawing the second match at Kingston.