Yuya Osako gave the home side the lead in the 12th minute when he peeled away from his marker to convert from Katsuya Nagato's corner, and Yuya Kuwasaki hit the second midway through the second half.
"I think it's extremely important to earn three points at home," said Osako, whose goal was his first in this season's competition.
"I'm happy we were able to get off to a good start and begin our home campaign on a positive note."
Kobe had dominated the opening exchanges and deserved to take the lead when Osako struck, but as proceedings wore on, Jeonbuk's threat increased.
Brazilian winger Italo cut the home defence open repeatedly after the interval, setting up Bruno Mota to hit the woodwork before substitute Lee Seung-woo headed inches wide of the Kobe goal.
Choi Woo-jin then struck the crossbar from distance before Kobe pounced on the counterattack, with Yoshinori Muto setting up Kuwasaki to sweep his 68th-minute shot past Song Bum-keun.
The win moved Kobe level with compatriots Kashima Antlers and Gamba Osaka as well as China's Beijing Guoan on six points.
Kashiwa Reysol thrash Port FC
Kashiwa Reysol picked up their first win of the campaign with a 5-1 thrashing of Thailand's Port FC as the Japanese hosts took a five-goal lead inside the opening half hour.
Tojiro Kubo put Kashiwa in front in the third minute before goals from Yuki Kakita, Riki Harakawa, Koya Yuriki and Hinata Yamauchi gave the home side an unassailable advantage by the 28th minute.
The first eight finishers in the 16-team league phase in both East and West Asia will qualify for the last 16, with the quarter-finals, semi-finals and final due to be played in Saudi Arabia in April and May.
