Bravo was the pick of the West Indies' bowlers with four wickets for 37 runs from 20 overs, and Collymore gave support with three for 27 from 17 overs, as India reached 235 for nine at stumps on Friday.
Several of India's batsmen got starts, but failed to carry on, and only captain Rahul Dravid playing a typically dogged knock showed prolonged resistance to top score with 49 for the visitors.
Dravid added 54 for the fourth wicket with left-hander Yuvraj Singh in the most significant partnership of the innings, but there was no substance and no stability from the rest of the batting.
It took a 47-run stand between Shantha Sreesanth and Anil Kumble to help India reach a respectable total, after they slumped to 180 for seven an hour into the final period.
Earlier, West Indies claimed the wicket of Venkatsai Laxman in the last 10 minutes before lunch to set back India on 74 for three at the interval.
Laxman was caught behind off Bravo for a workmanlike 29 driving loosely at a well-pitched outswinger, after he and Dravid spent the second half of the morning period trying to dig their side out of a sticky situation.
Openers Wasim Jaffer and Virender Sehwag were dismissed in the first hour, as the West Indies bowlers gained bounce and movement from the Antigua Recreation Ground strip.
Jaffer was caught behind off Fidel Edwards for one in the third over of the morning, and just before the drinks break, Sehwag was caught at second slip for 36 off Collymore.
Sehwag struck seven boundaries from 37 balls in a typically cavalier knock, including a few rasping leg-side strokes off the West Indies new ball pair of Edwards and Ian Bradshaw.
After lunch, India continued to grind away and reached 144 for four at tea break, after they benefited the partnership between Dravid and Singh.
The wheels fell off after tea for India though, with Bravo getting Kaif caught behind for 13 before Mahendra Dhoni edged a drive to second slip off Collymore to give Windies captain Brian Lara his 150th catch in Tests.
Two overs later, Dravid fell and it was left to Sreesanth and Kumble to beef up the Indian total. Two ferocious cuts off Edwards for fours from Sreesanth lifted Indian spirits and Kumble obliged with a few deflections of his own for boundaries before Bravo had him bowled for 21 off the inside-edge.
Bravo soon had Test newcomer Vikram Singh caught at extra cover for two, and West Indies could have wrapped things up had third-man fielder Mohammed held Sreesanth's skier off Edwards off the last ball off the penultimate over.
India, who have not won a series in the Caribbean since Ajit Wadekar's side achieved victory 35 years ago, surprisingly included left-arm fast-medium bowler Irfan Pathan and off-spin bowler Harbhajan Singh in the five they left out of their visiting 16.
The four-Test series between the two sides also features matches at Gros Islet (June 10-14), Basseterre (June 22-26), and Kingston (June 30-July 4).