Playing at Tan Sri Hassan Yunos Stadium in Larkin, JDT opened the scoring in the 14th minute through Syafiq Ahmad, who beat Selangor’s offside trap before slotting past goalkeeper Khairulazhan Khalid.
But three minutes later the visitors hit back to level the tie through Ifedayo Olusegun and the game remained 1-1 heading into the break.
JDT though was to have the last laugh after the break as former Argentina Under-20 international Leandro Velazquez settled things in the 49th minute.
The 30-year-old fired from outside the box and Khairulazhan could not stop the strike.
Both team will play the second leg next Saturday at Shah Alam Stadium.
In the other semifinal FA Cup champions Kedah were held 3-3 by Pahang at home in a barnstorming game.
Zaquan Adha Abdul Radzak was the hero for Kedah scoring the equaliser four minutes into extra time.
Pahang under the guidance of Dollah Salleh raced to a 2-0 lead through Wan Zaharulnizam Zakaria in the 13th minute before Dickson Nwakaeme converted a penalty in the 26th minute.
Kedah regained their composure and levelled the score through a brace from Spaniard Fernando Rodriguez in the 32nd and 39nd minutes.
Pahang retake the lead in the 73rd minute through Nor Azam Abdul Azih before Zaquan Adha came to Kedah’s rescue.
The second leg will be played at Darul Makmur Stadium, Kuantan next Saturday.