Herath, 38, surpassed the record of 362 wickets set by New Zealand’s Daniel Vettori as Bangladesh were all out for 197 on the final day of the first Test.
He has 366 wickets in 79 Tests, after finishing with match figures of 9-131, including six in the final innings.
He is second to only Pakistan’s Wasim Akram (414) of all left-arm bowlers.
In taking 6-59 in the final innings, Herath also claimed the 29th five-wicket haul of his career, drawing level with Australia’s Glenn McGrath.
Only Herath’s compatriot Muttiah Muralitharan (67), Australia’s Shane Warne (37), New Zealand’s Richard Hadlee (36) and India’s Anil Kumble (35), have taken more five-wicket hauls in Tests. (Courtesy BBC)