Warner and Gayle are one of 31 batsmen who have managed to cross 300 and the Australian's score on Saturday is two runs more than Gayle's highest Test score of 333 which he scored against Sri Lanka in Galle in 2010.
It was one of two triple centuries that Gayle scored in his illustrious Test career, the other being 317 against South Africa in 2005 in Antigua.
Warner is also the seventh Australian to score a triple ton. It is also the first time since December 2016 that any batsman has managed to score a triple ton in Test cricket after India's Karun Nair did so against England in Chennai.
Warner was unbeaten on 335 off 418 balls as Australia declared at 589 for 3. He shared stands of 361 for the second wicket with Marnus Labuschagne (162), a 121-run stand with Steve Smith (36) for the third wicket and an unbeaten 99-run stand with Matthew Wade for the fourth wicket.