The Japan right-back floated in a long ball from the right flank in the 67th minute in Gelsenkirchen, looking for Kevin-Prince Boateng, but managing to score his first goal in Europe and just second for the club since arriving from Kashima Antlers in 2010.
Uchida’s long, floating ball evaded teammate Boateng as well as Bucharest defender Lukasz Szukala and goalkeeper Ciprian Tatarusanu to nestle itself into the left corner to give Schalke the lead.
Boateng then added a second with a neat finish from an angle in the 78th minute before assist provider Julian Draxler made it 3-0 in the 85th minute with a deft chip after a clever ball from Christian Fuchs.
Schalke boss Jens Keller said: "That was a lucky goal, but sometimes you need something like that.
"We've made an excellent start in the Champions League this season.
"We kept another cleansheet, which makes me incredibly happy. We played patiently and had numerous chances. We didn't put enough pressure on them after the break, but we got the result we needed."