Marinos, runners-up in last season's campaign, had been handed a 7-3 thrashing by Gwangju FC in their first game of the current competition but made amends with goals from Kota Watanabe, Takuma Nishimura, Anderson Lopes and Kenta Mizunuma.
Current J-League champions Vissel Kobe also picked up three points when Takayuki Yoshida's side emerged 2-1 winners from a bad-tempered clash with Chinese Super League outfit Shandong Taishan.
The result moves Kobe onto four points from their opening two games of the league phase, two points behind Gwangju, who are the only team in the eastern side of the draw to win both of their matches so far.
Marinos overturned their recent poor form, having won once in their previous six games in all competitions, to claim a comprehensive victory over the current K-League leaders.
Watanabe put Marinos in front in the fourth minute, slotting in after a cut-back by Brazilian winger Elber.
Nishimura doubled the lead with a minute remaining in the half when he started and finished a blistering counterattack.
Lopes hit the third seven minutes from time with a left-foot shot from outside the area and Mizunuma completed the rout from close range in stoppage time.
"We've had a really tough run of results and some of the performances haven't been up to scratch, but I'm really proud of these boys because of their work ethic," said interim coach John Hutchison.
"Scoring four goals and a clean sheet at home, I'm very happy and it's a good way to push on."
Hosts Kobe picked up their first win having drawn 0-0 with Buriram United last month as goals from Taisei Miyashiro and Gotoko Sakai eventually saw off Shandong.
Miyashiro put Kobe in front with a 14th-minute header but Brazilian striker Cryzan levelled for the visitors when he nodded in a 28th-minute equaliser.
Sakai restored Kobe's lead six minutes into the second half when his strike took a deflection and looped over goalkeeper Wang Dalei.
The game descended into chaos at the end with the Shandong bench clearing on several occasions, and coach Choi Kang-hee was shown the red card deep into stoppage time.
The first eight finishers in the 12-team western and eastern divisions of the league phase advance to March's knockout rounds while the quarter-finals, semi-finals and final will be played on a centralised basis in Saudi Arabia in April and May.
