He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
The Sri Lankans won the game by 215 runs and took the series 1-0 after cutting off the Tigers at 123 on the third day of the Dhaka Test.
Dananjaya ended the game with 8 for 44, the best match figures by a Sri Lankan debutant. Rangana Herath four scalps in the second innings helped him reach 415 Test wickets and become the most successful left-arm bowler in the format.
Mominul Haque was the highest scorer in Bangladesh's second innings with 33.
The Sri Lankans had taken a 112 run lead after the Bangladesh lower order collapsed in the first innings. They posted an additional 226 in the second to set a target of 339 for Bangladesh.
But the loss of six wickets for 23 runs closed out a disappointing match for the Bangladesh batsmen.