Litton, playing his 111th T20I, began the match with 2,437 career runs and required just eight more to surpass retired Mahmudullah Riyad, who amassed 2,444 runs from 141 appearances.
With that milestone, Litton now sits behind only Shakib Al Hasan, the top run-getter for Bangladesh in the format with 2,551 runs in 129 matches.