Kashima were forced to play in Tokyo's National Stadium after their own ground was badly damaged in the 9.0-magnitude earthquake and tsunami which ravaged the country, stalling the domestic J-League season.
Tuesday's emotional Group H clash also took place in the early afternoon to avoid having to use floodlights, as part of a nationwide drive to avoid draining power from the crippled electricity grid.
A crowd of just over 4,600 saw South Korea's Suwon take the lead three minutes after half-time thanks to midfielder Yeom Ki-Hun's direct free-kick, which flew into the top corner.
But Kashima were level six minutes later when Yuzo Tashiro capitalised on a Takuya Nozawa free-kick.
Kashima appeared to have made it 2-1, but forward Shinzo Koroki's strike was ruled off-side. Koroki also blazed over in the dying seconds.
Antlers' Brazilian coach Oswaldo Oliveira said: "I expected them (Suwon) to play defensively and try to draw. I think they did as they planned. We missed two forwards and couldn't play our game. But we didn't give them many chances."
Suwon coach Yoon Sung-Hyo said: "Our team was not 100 percent because of injuries. I was disappointed that we failed to keep the lead, but I'm glad that we took a point from the draw."
Kashima are expected to play all their home games at the National Stadium until June at the earliest. The earthquake-hit J-League resumes this weekend.
Suwon remain top of Group H on goal-difference ahead of Kashima, who also have six points from four games.
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