The equaliser came in the 62nd minute, when second-half substitute midfielder Josef Martinez sent a cross from the right into the Japanese penalty area, where a falling Fedor found the net with his back toward the goal. Earlier, Endo, who hit the home side's first shot on goal, put Japan one up after defender Yuichi Komano sent a cross from the right to the centre of the penalty area, where Endo fired home a right footer in the 14th minute.
Endo also sent a pass from theto CSKA Moscow midfielder Keisuke Honda, who hit a sizzling shot from the edge of the area, only to see goalkeeper Daniel Hernandez make a fine reflex save in the 21st minute.
Venezuela played more aggressively after the break with Fedor, Mario Rondon and Luis Manuel Seijas threatening the Japanese goal mouth at the beginning of the second half.
It seemed that the home side had regained the upper hand with Makoto Hasebe, Honda, Ryoichi Maeda and Shinji Kagawa hitting shots consecutively shortly before Fedor made it even.
The Manchester United striker Kagawa, who missed a couple of headers, hit the bar in the 75th minute in what turned out to be the home side's last shot at victory.
"We scored early in the first half and it was not so bad, but we should have scored more as we had several more chances in the first half," said Japan coach Alberto Zaccheroni. "We also had several chances in the second half, but we slowed down a little bit."
Meanwhile, Kagawa said: "I really wanted to win, because it was a home game. I'm very disappointed as I had several chances. I want to take a win in the World Cup qualifying round next month."
Japan will take on Iraq in their next FIFA World Cup qualifying match on 7 September. They go in with seven points from two wins and a draw to lead Group B ahead of Australia, Iraq and Oman on two points each.
Venezuela, currently fifth in the nine-team South American competition with two wins, two draws and two defeats for eight points, will play Paraguay on 11 September.