Having overcome Lincoln Red Imps, Willem II and Galatasaray in the qualifying rounds – and fresh off an Old Firm triumph over Celtic – Steven Gerrard's side battled their way to three points in difficult conditions at Stade Maurice Dufrasne.
Tavernier scored the opening goal of the Group D contest in the 19th minute, Rangers' captain converting from the spot for his ninth goal in 10 outings this season.
The visitors relied on the crossbar to keep out a Jackson Muleka header before the break but were rarely troubled in a second half played out amid torrential rain, Roofe sealing a deserved victory when he spectacularly lobbed Arnaud Bodart from long range in stoppage time.
Connor Goldson had been the unlikely hero against Celtic, scoring twice in a 2-0 win at the home of their rivals, and the defender once again played a pivotal role with his aerial prowess.
It was his downward header from a corner that struck Nicolas Gavory on the arm, allowing the in-form Tavernier to tuck away the opportunity from 12 yards out.
Bodart was unable to keep the attempt out despite guessing the right way, though he did twice deny Alfredo Morelos early in the second half to keep the deficit down to one.
However, the goalkeeper was finally beaten again in the second added minute. Ex-Anderlecht forward Roofe pinched possession and, spotting the opportunity, lofted the ball over the out-of-position Bodart from inside Rangers' half.
What does it mean? Euro vision for Gerrard
Rangers did not manage to win on the road in the Europa League group stages in either of the previous two seasons.
However, Gerrard still engineered a route through to the last 16, where they lost to Bayer Leverkusen, in 2019-20. Their early form in this campaign, both at home and abroad, suggests they should be capable of going at least as far again.
Roofe fitter for late cameo
It was hardly surprising to hear a smattering of boos when Roofe was introduced. Indeed, his final goal during his time with Anderlecht had been against Liege. His stunning effort, converted from 54.6 yards – the furthest distance ever for a goal scored in the Europa League – silenced his critics in the stands, though, as he marked his return from a calf injury in sensational style.
Morelos' drought goes on
Morelos has scored eight Europa League goals for the club, not including qualification matches, but he has now failed to find the net in his last four appearances in the competition. He managed two shots on target but his first attempt should have been a pass instead, as the angle was tight and he had team-mates in support.
Key Opta Facts
- Rangers registered only their second away win in 11 attempts in the Europa League (D5 L4).
- After 15 home games unbeaten in European competition (including qualifiers), Liege lost their first home match since suffering a 3-0 defeat to Feyenoord in December 2014.
- Since their last defeat in August against Leverkusen, Rangers have won 12 and drawn two of 14 matches in all competitions, scoring 38 goals and conceding just four.
- Tavernier is Rangers’ top scorer in all competitions in the 2020-21 season with nine goals, scoring five of those nine from the penalty spot.
- Roofe has now scored three goals in his last five appearances for Rangers.