Shimron Hetmyer was batting on 10 with West Indies needing a solid rebuilding job from their middle order when play resumes.
The onus was on Kraigg Brathwaite and Kieran Powell to give the tourists a strong start after skipper Jason Holder won the toss and unsurprisingly elected to bat on a track that looked full of runs.
Besides, India paceman Shardul Thakur had also hobbled off the field with a groin injury after sending down only 1.4 overs in his debut test.
It was a combination of Powell's recklessness and Ravichandran Ashwin's guile which led to the first dismissal.
The opener stepped out against the off-spinner who quickly shortened his length and pitched it wide, prompting an uppish drive straight to Ravindra Jadeja at cover.
Kuldeep Yadav induced several edges that fell just short of Ajinkya Rahane at slip but the left-arm wrist spinner could not be denied for long.
Kuldeep dismissed Brathwaite for 14, trapping him lbw with a delivery that beat the bat and hit the opener on his back leg.
Hope hit five boundaries in his 36 but his dismissal off the final delivery before the lunch break tilted the session in India's favour.
Umesh generated movement off the seam to dismiss Hope leg before after a similar appeal against the batsman had been turned down in his previous over.
The tourists thumped inside three days by an innings and 272 runs in the Rajkot series-opener, made two changes with Holder returning from injury to replace Keemo Paul and spinner Jomel Warrican substituting Sherman Lewis.
India rested Mohammed Shami and handed a test debut to fellow paceman Shardul Thakur in the lone change to their side.
(With inputs from agencies.)