In the finals, they will take on Punjab, who got the better of the defending champions Uttarakhand 80-68.
Both teams were matching basket for basket throughout the match and Tamil Nadu were leading 55-36 at half time. Services reduced Tamil Nadu's lead to 16 in the third quarter.
Services managed to score 30 points in the final quarter but Tamil Nadu edged past them in the finals minutes of the game.
Pratham Singh scored 28 points (four 3-pointers), S P Venkatesh 22 (10 Rebounds), Rikin Pethani 14 (11 Rebounds) and P Akilan finished with 12 (two 3-pointers) for Tamil Nadu.
More From This Section
In the Punjab-Uttarakhand semifinal clash, Palpreet Singh and Ranbir Singh scored identical 27 points, while Gurwinder Singh added nine points for the winners.
Yadwinder Singh scored 24 points, Amritpal Singh 15 and Riyaz Uddin finished with 14 for Uttarakhand.
Meanwhile, Chhattisgarh women, who lost to Maharashtra in the league stage, avenged their defeat by posting a 76-65 win against in their semifinal clash.
Leading 33-20 at half time, Kavita scored 20 points (11 Rebounds), Deepa L 16 (two 3-pointers), Seema Singh 14 (13 Rebounds), Poonam Chaturvedi 10 (10 Rebounds) and Bharati Netam (one 3-pointer) finished with 10 for Chhattisgarh.