Opener Virat Singh (43 off 31) and Ishank Jaggi (33 off 36) helped Jharkhand reach 163 for six in 20 overs.
Tripura began the chase well through Smit Patel (49 off 37) and Udiyan Bose (29 off 24) before Jharkhand bowlers bounced back to limit the opposition to 139 for nine.
Captain Varun Aaron, Shahbaz Nadeem and Kaushal Singh took two wickets each for the home team.
In the other East Zone match, Odisha beat Assam by 51 runs.
The bowling stars for Odisha were Abhishek Raut (3/14) and Prayash Singh (3/6).