The former Chelsea midfielder had scored in his previous four appearances in the continental competition, but could not add to his tally.
Shanghai fell behind a minute before half-time in their Group F clash as Rafael Silva pounced on a loose ball to fire across Yan Junling.
The Chinese Super League side were given two chances to salvage something from the clash, but Oscar – the most expensive CSL signing – could not take advantage.
His first opportunity came after 65 minutes when he was hauled down in the area, but Shusaku Nishikawa made a superb save to palm it onto the crossbar.
Nishikawa did not need to do anything with the second spot kick 11 minutes later, as Oscar blazed it over the bar after Tomoaki Makino had handled.
The result moved Urawa above Shanghai and into top spot in the group, but Oscar's side are still well placed to qualify, with a six-point cushion over third-placed Seoul – who beat Western Sydney Wanderers 3-2 thanks in part to a Dejan Damjanovic double.