The duo, who often torment teams with long and stubborn innings, both completed half-centuries to steer India to a commanding position of 229 for three in their second innings at stumps on the fourth day at Kensington Oval.
That gave the tourists an overall lead of 240 with seven wickets in hand and only one day remaining in a low-scoring match that has been interrupted by torrential rain but may yet produce a result.
While a draw still looms as the most likely result, India at least appeared to be out of any danger and building toward a position where they could set up an early declaration on the final day.
Laxman, who top-scored with 85 in the first innings, finished the day unbeaten on 72 with Virat Kohli on 26. The pair added 75 for the unbroken fourth wicket without taking any risks or trying to increase the run-rate.
Laxman had also shared a 65-run stand with Dravid, who made 55, after his patient hundred in last week’s first test in Jamaica gave India their 1-0 series lead.
Dravid also batted cautiously after surviving a let-off on nine when he spooned a catch to Adrian Barath at midwicket, the fielder tumbling sideways to claim a low catch.
Dravid stood his ground and, as is almost always the case with low catches, the slow-motion video replays proved inconclusive so he was given the benefit of the doubt.
India started the day on 23 for no wicket, adding 206 runs, for the loss of a wicket in each session.
Opener Murali Vijay departed early for three when he feathered a catch to wicketkeeper Carlton Baugh off paceman Ravi Rampaul, then Abhinav Mukund went for 48 after lunch when he gloved a catch behind off a bouncer from Fidel Edwards.
