The hosts now lead by 81 runs with four second innings wickets in hand.
Earlier, India's ace spinner Harbhajan Singh sent back centurion Edwards, and then followed it up with the wicket of Marlon Samuels in the same over as the Indians hit back.
Edwards was caught behind by India skipper Mahendra Singh Dhoni for 110, and Samuels followed suit soon after for a duck as he was adjudged leg before wicket, though replays suggested that the ball would have gone on to miss the off stump.
Edwards put on 161 runs for the fourth wicket with Shivnarine Chanderpaul and became the 14th West Indian to score a Test century on debut.
Chanderpaul brought up his 56th half century as the home team marched on after tea.
Edwards brought up his maiden Test fifty, and was involved in an unbeaten stand of 76 runs with Chanderpaul as the West Indies went into tea at 116/3.
The hosts lost their third wicket after lunch when Darren Bravo's attempt to hit Harbhajan Singh out of the ground only went as far as Praveen Kumar at the wide mid-off region who took a comfortable catch.
Bravo made 14 and was involved in a 30 run partnership with Chanderpaul.
India's new ball bowlers, Ishant Sharma and Praveen Kumar struck early by removing the West Indian openers in their second innings as players took lunch. While Adrian Barath fell to Kumar for six, Kieron Powell was snapped up by Sharma after making just four.
Edwards on seven and Bravo on nine were at the crease after a pulsating first session which witnessed the loss of six wickets drew to a close.
West Indies pace bowler Fidel Edwards grabbed his 10th five wicket haul in the traditional form of the game as the Indian innings folded up for 347.
Carrying on from their overnight score of 308/6, the visitors added 39 more runs to take a healthy lead of 143 before being bowled out.
Harbhajan was the first man to be dismissed this morning when he top edged a pull shot only to be caught by Windies wicketkeeper Carlton Baugh who took a fine running catch. Harbhajan made no addition to his overnight score of 12.
Indian skipper Mahendra Singh Dhoni was the next batman to depart after a short rain break when he pulled a delivery from Edwards straight into the lap of Devendra Bishoo at the deep square leg boundary. Dhoni made 74 which was the highest score in the Indian innings.
India lost their ninth and tenth wickets when Praveen Kumar and Ishant Sharma fell in quick succession.
Kumar was caught by Marlon Samuels after scoring a quickfire 23 off 27 balls, hitting a six and a couple of fours on the way.
Sharma was the final Indian wicket to fall as he failed to deal with a rising ball from Edwards to be caught by Adrian Barath for two.
Edwards returned with figures of 5/103 and took three of the four wickets to fall on day four.
