Shanghai came through a thrilling quarter-final with Chinese Super League rivals Guangzhou Evergrande on penalties to reach the last four.
And they made a strong start against their J1 League opponents as Hulk broke the deadlock in the 15th minute with a fierce effort from outside the area.
Shanghai were pegged back 13 minutes later by Yosuke Kashiwagi with the visitors' only shot of the game and, despite dominating, Andre Villas-Boas' men were unable to re-establish their advantage.
Hulk opened the scoring after a quarter of an hour by capping a surging run with a low drive that flew beyond Shusaku Nishikawa and into the bottom-right corner.
But Urawa responded with an impressively worked goal, Takuya Aoki lofted the ball into Shinzo Koroki's feet and his lay off was met by Kashiwagi, whose half-volley escaped the grasp of Chen Wei.
Oscar saw a curling effort beaten away by Nishikawa and Wu Lei headed wide on the follow-up as Shanghai continued to pressure the Urawa goal after the restart.
Odil Ahmedov shot narrowly wide 10 minutes into the second half but the best chance to restore Shanghai's lead fell to Brazil international Oscar.
The former Chelsea midfielder was denied by the woodwork as his curling free-kick struck the right-hand post, leaving Shanghai definitely needing to score to seal a place in the showpiece.