Shinzo Koroki cancelled out Salem Al Dawsari's first-half opener for the hosts and, with the away goals rule in use, the Japanese side will be marginal favourites to claim the title when the teams meet again at Saitama Stadium on Saturday.
Urawa's hopes were enhanced further when Al Dawsari was sent off with three minutes remaining after he kicked out at Ken Iwao while the pair lay on the turf following an earlier tussle.
The red card means Al Dawsari will miss the second leg.
The clubs are meeting in the Asian Champions League final for the third time in six years and, despite Al Dawsari's impending absence, the tie is evenly poised going into next week's decider.
A crowd in excess of 53,000 turned out as Al-Hilal set their sights on a record-extending fifth Asian crown and saw Al Dawsari give their side the lead after 13 minutes.
The Saudi Arabia international pounced at the far post after Brazilian winger Michael had evaded left back Takahiro Akimoto to drive a low centre across the face of goal.
Indecision saw goalkeeper Shusaku Nishikawa and defender Alex Scholz leave the ball for one another, with the hesitation allowing Al Dawsari to strike left-footed into the roof of the net unchallenged.
Urawa had carried little threat in the opening 45 minutes but levelled the scores eight minutes into the second half through an opportunistic Koroki strike.
Defender Ali Al Bulayhi's attempt to intercept Tomoaki Okubo's pass into Koroki's path flew towards the Al Hilal goal, thumping off Abdullah Al Muaiouf's right post and rebounding towards the on-rushing Koroki, who slotted home.
Moussa Marega was denied midway through the second half when Nishikawa reacted quickly to touch the Mali international's shot on the turn narrowly wide before Al Dawsari's moment of madness left Al Hilal playing with 10 men for the dying moments.
Urawa host the second leg next Saturday aiming to win the Asian title for the third time after victories in 2007 and 2017.
