Taiki Hirato's fortunate opener two minutes before the break - when his attempted cross bounced past goalkeeper Farizal Marlias - and a Serginho strike from distance 11 minutes into the second half settled the contest in Kashima's favour.
Coach Go Oiwa fielded a weakened side in Kashima's first group game since winning the title at the end of last year and the eight-time J-League champions should have been ahead by the 14th minute but Brazilian striker Serginho's penalty was saved.
After Hirato and Serginho struck for Kashima, Brazilian striker Diogo pulled one back 10 minutes from time for the Malaysian champions, but Oiwa's side closed out the game to take all three points in the Group E encounter.
"You never know what's going to happen in any game in this tournament and that's something I told our players," said Oiwa.
"The way we played and how we controlled the game, we shouldn't really be giving chances to the opposition. Now, we have to refocus our mind and move on to the next game."
Kashima top the group standings after Graziano Pelle's double earned Shandong Luneng a 2-2 draw with South Korea's Gyeongnam FC, the Italian netting his second goal 13 minutes from time to claim a point for the Chinese Super League side.
In Group F, former champions Guangzhou Evergrande had first-half goals from Anderson Talisca and Paulinho to thank for a 2-0 win over Japan's Sanfrecce Hiroshima, while South Korea's Daegu FC fell behind to an Ola Toivonen goal but fought back to hand Melbourne Victory a 3-1 defeat.
Daegu's Brazilian striker Cesinha thumped an effort from distance past keeper Lawrence Thomas to level just after the half hour mark before Hwang Soon-min's heavily deflected effort gave the Koreans the lead and Edgar completed the win.
In the west of the continent, a rampant second half performance from twice champions Al Ittihad saw the Saudi Arabia side hand Qatar's Al Rayyan a 5-1 thrashing in Group B.
World Cup striker Fahd Al Muwallad struck twice for the Jeddah club, who were joined on three points by Uzbekistan's Lokomotiv Tashkent after their 2-0 victory against Al Wahda of the United Arab Emirates.
Al Wasl fared better than their UAE compatriots as they notched up a 1-0 win over Saudi Arabia's Al Nassr with a Fabio Lima goal as Laurentiu Reghecampf's team lead Group A after Zobahan from Iran and Iraq's Al Zawraa shared a 0-0 draw.
