Gayle was dismissed for 83 and Ganga was unbeaten on 64, as West Indies, choosing to bat, reached 207 for one in their first innings when stumps were drawn on the rain-marred opening day.
Gayle was typically belligerent and Ganga batted doggedly to share 143 for the first wicket, after play commenced two-and-a-half hours later than scheduled.
After Gayle was dismissed about a half-hour after tea, Ganga and Ramnaresh Sarwan, who is not out on 44, continued to defy the Indian bowlers and added an unbroken 64.
Not a ball was bowled before lunch which was taken 10 minutes earlier than scheduled, after overnight and early morning showers drenched the outfield and left several areas close to the boundaries sodden.
After a series of inspection during the morning, umpires Rudi Koertzen and Brian Jerling indicated that play would commence immediately after lunch, and a minimum of 70 overs were to be bowled in the day.
The number of overs was further reduced to 64 when there was a 25-minute stoppage for rain about a half-hour after play started, but this could not stop the West Indies onslaught.
Gayle raced to a half-century before tea to help West Indies reach 108 without loss at the break.
The left-handed Gayle drove off-spin bowler Harbhajan Singh through extra cover for the fourth of his eight fours to reach 50.
When on five, Gayle lofted Shantha Sreesanth over long-on for the first of his five sixes onto the roof of the Media Centre to reach 4,000 runs in his 60th Test.
Ganga, who was fortunate to have retained his place in the side following a string of insignificant scores in the series, was a passenger for most of the way, although a straight drive for four off Munaf Patel was memorable.
After tea, Gayle continued on his merry way and was eyeing his eighth Test hundred when he miscalculated the length and line of a delivery from Munaf Patel, and was bowled offering no stroke to his 128th ball.
Ganga was then 47 and spent what seemed an eternity on that score before reaching his half-century when he turned a delivery from Anil Kumble into the fine leg region for a single.
Both he and Sarwan, strugglers in the previous two Tests at St John's and Gros Islet, showed grit and determination in the final hour when they survived a number of raucous appeals from the Indian bowlers in the closing overs.
West Indies made one change to their side, with batsman Marlon Samuels replacing left-arm medium-fast bowler Ian Bradshaw.
India, on the other hand, brought Harbhajan and Sreesanth into their 11 for Irfan Pathan and Vikram Singh.
The four-Test series is still level at 0-0, after the first two Tests at the Antigua Recreation Ground and the Beausejour Cricket Ground ended in tense draws.
The series concludes at Kingston's Sabina Park from June 30 to July 4.
Warner Park is staging its first Test and has become the ninth Test venue in the West Indies and the 94th in the World.
Scoreboard at stumps on the rain-affected opening day in the third Test between West Indies and India on Thursday at Warner Park:
West Indies 1st Innings
To bat: B. Lara, S. Chanderpaul, D. Bravo, M. Samuels, D. Ramdin, P. Collins, J. Taylor, C. Collymore
Fall of wickets: 1-143
India: V. Sehwag, W. Jaffer, V. Laxman, R. Dravid, Y. Singh, M. Kaif, M. Dhoni, H. Singh, A. Kumble, S. Sreesanth, M. Patel
Toss: West Indies
Umpires: R. Koertzen, B. Jerling, Third Umpire: C. Mack
Reserve: L. Kelly
Match Referee: J. Crowe