Bulut gave the Wanderers a dream start before Go Yohan equalised late, brilliant saves by both keepers ensuring the scores remained level in a frenetic finish.
With both sides level behind group leader Guangzhou Evergrande, a win at Parramatta Stadium would have put the Wanderers in the box seat to progress with the top two teams to go through.
Instead the Wanderers remain in second spot but only ahead of FC Seoul on goal difference, four points behind Guangzhou after it lost 2-1 at Kashima Antlers.
The Wanderers' next match against bottom-placed Kashima Antlers at Parramatta Stadium in a fortnight now looms as a must win for the reigning champion to go through.
After a slow opening to the contest Western Sydney broke through with its first genuine attack.
The Seoul defence failed to deal with a long ball from Iacopo La Rocca and the misplaced clearance fell right into the path of Kerem Bulut.
The striker placed his first-time shot inside the post to give the Wanderers a 1-0 lead on 12 minutes.
The visitor began the second period with more attacking intent. On 54 minutes Colombian Mauricio Molina found space on the edge of the area and fired a shot that cannoned down off the crossbar and agonisingly close to the Wanderers goal line.
Seoul pressure finally paid off in the 72nd minute as Cha Du-Ri played Everton through in the area. The Brazilian cut the ball back across goal and substitute Ko Yo-Han was on hand to tap in and pull the Korean side level.
Western Sydney still looked dangerous in attack, particularly the lively Bulut. A fiercely hit shot from an acute angle forced an excellent save from Kim Yong-Dae shortly after the equaliser.
The Wanderers had shouts for a penalty turned down after substitute Tomi Juric appeared to have been pulled to the ground in the box by Cha.
Both sides had excellent chances to win it late on.
Ante Covic pulled off the save of the match in the dying stages. The goalkeeper was airborne to diffuse a heavily deflected volley with replays showing he took the ball over the line with him.
Kim was also under fire at the other end, denying both Romeo Castalan and Jason Trifiro in the final minutes.
Western Sydney and Seoul will now rely on their last two matches to try and clinch one of the top two spots in the group and qualification for the last 16.
Wanderers coach Tony Popovic admitted the hectic schedule caught up with his weary side which lost momentum after the interval.
"After that second half it could have gone either way, but the first half we totally dominated," he said.
"It was very pleasing for us to see what we can do this at this level. We hurt them in behind, we controlled the tempo, we kept the ball.
"The only disappointing thing is we're not going in two or three up at halftime and then I think fatigue set in for us.
"But we've played four games against them now and they've yet to beat us. So we're not doing too bad."
FC Seoul coach Choi Yong Soo praised his side's performance.
"We played the defending champions and had a difficult game in the first half but my players showed the passion to win the second half," he said.
"With two games to go we will play to go through the group of death."
