The visitors took the initiative and broke the deadlock shortly before the quarter-hour mark, when a flicked touch from skipper Bryan Cristante following a corner-kick was headed home from close-range by Matias Soule for his first UEL goal of the season.
To Rangers’ credit, they responded well to the setback, and almost equalised through Youssef Chermiti not long afterwards, but his shot from inside the penalty area was dragged just wide of the target.
The Giallorossi took advantage of some static Rangers defending to double their advantage in the 36th minute, as Artem Dovbyk teed up Lorenzo Pellegrini beautifully before the Italy international placed the ball confidently past Jack Butland into the bottom corner.
It could have got even worse for Danny Röhl’s side on the stroke of HT, with Soulé’s strike from just outside the edge of the box whistling narrowly wide of the post.
Roma appeared to take their foot off the gas after the interval while Rangers continued to search for a lifeline.
Mikey Moore saw a promising effort go wide in the 58th minute, while Chermiti hit the side-netting from close-range when he should have at least forced Mile Svilar into action.
With 20 minutes remaining, the visitors should have killed the game off completely, yet Zeki Çelik inexplicably hit the bar from inside the six-yard box.
Rangers continued to work hard and threatened once again, this time through Danilo, but his shot was superbly blocked by Svilar to keep his clean sheet secure. Ultimately, the damage had already been done by half-time.
Gian Piero Gasperini’s side had lost two UEL matches in a row heading into this game, so the three points in Glasgow will be a welcome relief to all Giallorossi supporters. Roma’s victory sees the Italian giants move up into the top 20 at the halfway stage of the league phase.
Danny Röhl’s team, meanwhile, remain rooted to the bottom of the table and are still searching for their first point.
Flashscore Man of the Match: Matias Soule (AS Roma)