The visitors created the initial chances, with shots from Steven Berghuis, Orkun Kökcü and Sam Larsson, but Rangers otherwise dominated proceedings in the opening 45 minutes. The hosts brewed up a storm, with Feyenoord constantly under pressure.
Rangers were awarded a penalty just 10 minutes in, but home skipper James Tavernier was unable to convert it. The goal eventually came on 24 minutes. Sheyi Ojo dispossessed Rick Karsdorp before letting rip from 20-plus metres out. His bullet went into the top left-hand corner.
The way the match was panning out suggested that would not be the only goal of the night. Rangers continued to press and create chances, and Ojo went close to doubling his tally with a shot that was cleared off the line by Eric Botteghin before the break.
The Scots were lacking precision, however, and as the second half wore on, Feyenoord started to play. With Luciano Narsingh, Nicolai Jørgensen and Jens Toornstra on from the substitutes’ bench, the visitors found their rhythm and began to pass it around. Gilt-edged chances remained elusive, though.
The best opportunity came not long after the break. The hosts lost track of Botteghin at a corner, but the Brazilian was unable to direct his header. Narsingh was also dangerous, forcing a save from keeper Allan McGregor.
The loss leaves Feyenoord playing catch-up in Europa League Group G, with Rangers FC leading the way with FC Porto. The Portuguese outfit beat Swiss side Young Boys 2-1 in their opening fixture. Next up for Feyenoord is a visit to FC Emmen on Sunday (kick-off 14:30 CET).