Nguyen Abou Leygley Minh's own goal in the 61st minute kept the J-League champions perfect after Toru Oniki's side started their campaign by thrashing Newcastle Jets last month.
Kashima lead compatriots Gamba Osaka, who also secured a second win in a row when Tomokazu Myojin's team came back from a goal behind to win 3-1 against Newcastle in Australia.
Nikos Vergos gave the Jets a 32nd-minute lead with a heavily deflected strike from the edge of the area, but Yusei Toshida's header eight minutes later levelled the scores.
Deniz Hummet, who scored the winner when Gamba beat Saudi Arabia's Al Nassr to claim last season's Asian Champions League Two title, hit the decisive second with 17 minutes remaining, and Welton Felipe rounded out the win with a late third.
Fabio Abreu's 79th-minute header earned Beijing Guoan a 1-0 win over hosts Buriram United in Thailand as the Chinese Super League outfit also secured their second successive victory.
Japan's Kyoto Sanga defeated Ratchaburi from Thailand 1-0 to pick up their first three points of the campaign through Temma Matsuda's 88th-minute volley, while Shanghai Port were held to a 1-1 draw by Daejeon Citizen.
Prince Ampem had given hosts Shanghai a 49th-minute lead, but Diogo Oliveira headed in from close range five minutes later to earn the South Korean side a share of the points.
Marcos Guilherme scored twice as Malaysian champions Johor Darul Ta'zim took advantage of Pohang Steelers midfielder Jeon Min-gwang's sending off just before the break to win 2-0.
Guilherme put the visitors ahead four minutes after the restart before sealing the points for Xisco Munoz's side with his second a minute from time.
The first eight finishers in the 16-team league phase in both East and West Asia will advance to the knockout rounds of the competition, with the tournament's quarter-finals, semi-finals and final to be played in Saudi Arabia next April.