Kim Ju-sung's dismissal for a second bookable offence in the 26th minute in Johor left the Japanese side short-handed and the Malaysian champions took full advantage through second-half goals from Ager Aketxe, Bergson da Silva and Marcos Guilherme.
"We're very happy with the result," said Aketxe. "The red card for Hiroshima gave us an advantage but our team was very committed and worked hard.
"Because of the goal we conceded, we need to keep working and be ready for the second leg."
Kim was sent off when he caught JDT midfielder Nene in the face with a flailing arm and the Japanese side succumbed in the heat and humidity of southern Malaysia.
Aketxe put JDT in front with an unerring strike past Keisuke Osako in the 52nd minute as the Hiroshima defence only partially cleared Nacho Mendez's corner.
Eleven minutes later the home side doubled their lead, Bergson finding the top corner after Eddy Israfilov's cutback and Guilherme added the third when he finished off a blistering counter-attack.
Nene's late own goal as the JDT defence failed to clear Shuto Nakano's long throw gave Hiroshima a glimmer of hope ahead of the return clash in Japan next Wednesday.
Vissel Kobe, meanwhile, will take a one-goal advantage into the second leg of their last-16 meeting with FC Seoul after defender Matheus Thuler scored the only goal in South Korea.
The Brazilian stooped to nod the ball over the line from close range in the 23rd minute to give Michael Skibbe's side a slender advantage.
The quarter-finals, semi-finals and final of the Asian Champions League Elite are due to be played in a centralised format in Jeddah in April although the ongoing crisis in the Middle East has thrown the schedule into doubt.
Last-16 matches that were due to be played in west Asia this week and next have been postponed following the attacks by the US and Israel on Iran.