Their partnership is now the highest for the sixth wicket or lower in Test cricket. The previous record was 399 runs, set by England’s Ben Stokes and Jonny Bairstow against South Africa in Cape Town in 2016.
Jangoo scored 233, while Chase made 194.
The stand was also the first 400-plus partnership for the sixth wicket or lower in Test cricket history.
Jangoo reached another milestone by becoming the 11th West Indies batter to convert his maiden Test century into a double century. His 233 is the fifth-highest score among those 11 players, behind Gary Sobers (365), Brian Lara (277), Rohan Kanhai (256) and Faoud Bacchus (250).
The left-hander also created another record. He now has three first-class centuries, and all three have been converted into double hundreds, making him the first batter to achieve that feat.
Chase, meanwhile, fell just six runs short of his maiden Test double century. His 194 was his sixth Test hundred, his first in seven years and the highest score of his career.
Sri Lanka were left with four overs to bat before stumps. They lost Pathum Nissanka in the second over and ended the day on 15 for 1, still trailing by 303 runs. Kasun Rajitha was unbeaten on 4, while Nishan Madushka was not out on 2.
Nissanka had a disappointing match, following his first-innings score of 2 with another low score of 3. He had made 158 in his previous Test against Bangladesh.
West Indies had resumed the day on 271 for 5, still 37 runs behind Sri Lanka’s first-innings total of 308. Jangoo was unbeaten on 78 overnight, while Chase resumed on 42.
The pair, who came together before tea on the second day, batted through the entire first and second sessions on day three. Jangoo, playing only his second Test and filling in for the injured Shai Hope, improved on his previous highest Test score of 30.
He reached his double century in 342 balls and needed only 116 deliveries to move from his maiden Test hundred to 200. His innings included 17 fours and one six.
The pair added 85 runs in the first session on Saturday and followed it with another 136 runs in the second session.
Jangoo’s innings ended when he was caught off a top edge from Milan Rathnayake, one ball after hitting the same bowler for a six over deep backward square.
Chase looked set for a double century after his partner’s dismissal but was bowled by Sonal Dinusha while attempting a sweep shot, finishing six runs short.