Kevin Muscat's CSL leaders Shanghai Port slumped to a 3-0 loss against Pohang Steelers while Johor Darul Ta'zim beat visitors Shenhua 3-0 in Malaysia.
Thailand's Buriram United, meanwhile, defeated Australian champions Central Coast Mariners 2-1 in Gosford to pick up their first win of the campaign.
Gwangju followed up their 7-3 thrashing of Yokohama F Marinos on the opening day with a gritty victory over Kawasaki, with Jasir Asani's 21st-minute penalty earning Lee Jung-Hyo's side another three points in the league phase.
Goalkeeper Kim Kyeong-min ensured Gwangju held onto the points as Frontale pushed for an equaliser, with substitute Erison also hitting the post late in the game for Kawasaki.
Malaysian champions JDT brushed aside Shanghai Shenhua, with Arif Aiman and Jorge Obregon scoring inside the opening 26 minutes to give the home side a comfortable lead.
Juan Muniz hit the third 10 minutes from time with a perfectly executed free kick to move his side onto four points after an opening 2-2 draw with Shanghai Port last month.
"These three points are very important because we capitalised on the one point we got away in the first game," said JDT head coach Hector Bidoglio.
"Today JDT showed at home we're a difficult team to beat."
Buriram United joined JDT on four points with their 2-1 win over Central Coast having drawn 0-0 with Vissel Kobe in the first round.
Guilherme Bissoli put the Thai League 1 champions in front when he directed Dion Cools' cross past Adam Pavlesic and Curtis Good doubled the advantage five minutes into the second half with a header.
Pavlesic was sent off for hauling down Bissoli in the 57th minute while Lucas Mauragis' strike into the top corner in the fifth minute of stoppage time was little more than a consolation for the hosts.
Pohang bounced back from their opening day loss to Shanghai Shenhua with a strong second-half showing at home to defeat Shanghai Port, with goals from Wanderson, Hong Yun-sang and Han Chan-hee delivering a 3-0 victory.
The second round of matches in the league phase will be completed on Wednesday when Japanese champions Vissel Kobe host China's Shandong Taishan and last season's runners-up Yokohama F Marinos entertain Ulsan HD.