In a low-scoring encounter, Sri Lanka looked in big trouble as they slumped to 50 for six in pursuit of Bangladesh's 120 all out at the Zahur Ahmed Chowdhury Stadium in Chittagong.
However, star man Kumar Sangakkara edged the tourists closer to their target with a run-a-ball 37 before Thisara Perera (35 not out) and Senanayake (12no) took them past the winning post.
For the second time this week the match was in the balance right until the last delivery, with Sri Lanka needing two runs for the win, and Senanayake was his side's hero as he turned Farhad Reza to the boundary for the match-winning runs.
Sri Lanka, the top-ranked T20I side in the world, also won another thriller right at the death on Wednesday when they clinched a two-run victory here in the opening encounter after defending a total of 168 for seven.
Perera bowled the final over on that occasion, dismissing Anamul Haque for 58 off the last ball having been hit for 14 off the previous five balls, but it was his batting which proved key on Friday.
After five of Sri Lanka's top seven batsmen had fallen for single-figure scores, Perera and Sangakkara helped get their side back into the game with a 46-run partnership - the highest in the match - before the latter was dismissed by Rubel Hossain with 25 runs still needed.
At that point Bangladesh must have felt the game had swung back their way, but Perera and Senanayake took it away from them again as Sri Lanka added the T20 series to their Test triumph over the same opponents.
Earlier, Bangladesh had been bowled out for 120 off the penultimate ball of their innings. Sabbir Rahman (26) and Haque (24) were the only players to get into the 20s as Lasith Malinga (three for 20), Senanayake (two for 11) and Nuwan Kulasekara (two for 32) prevented the hosts from cutting loose.
The two nations will now do battle in a three-match one-day international series.
- Sports & Recreation
- Thisara Perera
- Kumar Sangakkara
- Zahur Ahmed Chowdhury Stadium
- Sri Lanka