Chasing a highly improbable, if not impossible victory target of 392, West Indies ended on 298 for nine with their last wicket pair of Edwards and Collymore defying all India had to throw at them in the closing overs.
It all came down to the final over of the match, and Collymore, who has little pretensions of being a batsman, resisted Shantha Sreesanth to leave the four-Test series level at 0-0.
A career-best 52 from Dave Mohammed and his 51-run stand with left-hander Ian Bradshaw eased the nerves of West Indians too accustomed to their side conceding matches after holding healthy positions.
Umpire Asad Rauf dubiously adjudged Bradshaw caught behind for 10 when he drove at a delivery from Munaf Patel with 10.4 overs remaining, but television replays showed his bat came nowhere near the ball and had clipped his pad.
Mohammed, whose outrageous batting had won him as many admirers as he had detractors, reached his 50 when he edged Anil Kumble past Rahul Dravid, the Indian captain, at slip for four.
Kumble however, got his revenge, when he bowled Mohammed to leave West Indies on 297 for nine, and Edwards and Collymore, village-mates in their native Barbados, to resist the rest of the way.
Kumble was India's most successful bowler with four wickets for 107 runs from 34 overs. Virender Sehwag, bowling his uncomplicated off-spin, snared two for 39 from 11 overs, and Sreesanth took two for 49 from 19 overs.
Chris Gayle and Shivnarine Chanderpaul carried West Indies to 158 for three at the tea break, and appeared to be taking them to safety, but the wheels fell off in the first 10 overs after the interval.
Kumble snared the wickets of Gayle, for the top score of 69, and Chanderpaul for a supporting knock of 62 that included 10 boundaries from 109 balls, to transform the complexion of the match and expose the tail.
Gayle was dismissed in the third over after the tea break, when he played a long way forward and umpire Simon Taufel adjudged him lbw. This broke his stand for the fifth wicket with Chanderpaul that added a valuable 99 and halted the slide that saw West Indies reach 72 for three at lunch.
After tea, Chanderpaul reached 50, when he pushed Kumble to mid-off for a single, and he might have been eyeing something more significant, but a dubious decision from umpire Simon Taufel cut him short.
The former West Indies captain was adjudged caught at first slip, when he drove at a full length delivery from Kumble, but television replays showed the ball had clearly come off the pad.
When Chanderpaul departed, West Indies still had a minimum of 30 overs to navigate, and this prompted a mini collapse.
Chanderpaul was the first of three wickets that went down for 18 runs in the space of 39 balls.
Dwayne Bravo was caught behind for 28 off Sehwag edging a forward defensive probe, and Denesh Ramdin was caught at slip for eight off the same bowler top-edging a cut to leave West Indies 226 for seven.
Mohammed came to the crease and, despite the urgings of the crowd and Bradshaw, he batted with some recklessness.
He added 51 for the eighth wicket with Bradshaw, before another dubious umpiring decision gave India the breakthrough.
But try as they might, India just could not put the game to bed and the Windies held on for a morale-boosting draw.
India, rated at three on the latest International Cricket Council Test Rankings, are seeking their first series victory in the Caribbean for 35 years.
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).
Final scoreboard on the fifth and final day in the opening Test between West Indies and India on Tuesday at the Antigua Recreation Ground.