Goals from Joo Min-kyu and Hwang Il-su gave the South Korean side a precious lead and two away goals to take home for the second leg in a week's time.
In a battle of former Asian champions, home side Urawa dominated possession in the first half and were rewarded when Kenyu Sugimoto got on the end of a delightfully chipped ball from Takuya Aoki in the 37th minute, and his glancing header found the bottom left corner.
Ulsan had hardly threatened till that point, but it took them just five minutes to get back on terms.
A mistake in midfield enabled the lively Lee Keun-ho to burst down the left flank and drive in a cross, which was met by a powerful header from Joo that flew back across goalkeeper Shisaku Nishikawa and into the top left corner.
The goal lifted the visitors, who grew into the match in the second half with the lively goal provider Lee twice going close to putting Ulsan ahead.
First a rasping volley from the edge of the box flew just wide then a near-post flick found the side netting.
Then Lee was substituted by Brazilian striker Junior Negrao in the 74th minute as Ulsan went in search of a winner.
Instead, six minutes later it was another Ulsan substitute, Hwang, who ran unopposed to the edge of the penalty area as the Urawa defense backed off, before rasping home a left-foot shot.
Junior should have made it three shortly after, but somehow cleared the crossbar from six yards out as Ulsan held out.