The six potential highest-ranked opponents Steven Gerrard’s men could be paired with in next Monday’s third qualifying round draw - Bulgarian champions Ludogorets, Swedish side Malmo, Cluj of Romania, Polish champions Legia Warsaw, Ferencvaros of Hungary and Moldovan champions Sheriff Tiraspol - all justified their seedings to come through their opening ties.
But an element of uncertainty remains before Rangers will know who they face over two legs at the start of August.
There will still be an ‘either/or’ element to the draw as all six of those aforementioned clubs still have to come through their second qualifying round ties, the first legs of which take place next week.
Shock results at this stage of the competition are not unknown and some of the six lowest-ranked clubs in the ties relevant to Rangers will fancy their chances of upsetting the odds.
The Scotsman looks at the six potential curveballs which could yet come the way of the Scottish champions.
After a financial collapse in 2013, Mura climbed from the fourth tier back to the top flight of Slovenian football before winning the title for the first time in their 97-year history last season.
They defeated North Macedonian champions Shkendija 6-0 on aggregate in the first qualifying round and now face Ludogorets.
The Lithuanian champions have a familiar face still prominent in their side in the shape of former Hearts favourite Saulius Mikoliunas.
Now 37, the winger scored the opener in Zalgiris’ 2-1 win at Linfield on Tuesday night to complete a 5-2 aggregate win in the first qualifying round tie and secure a second round clash with Ferencvaros.
The Finnish champions are well into their 2021 domestic season and crushed Buducnost of Montenegro 7-1 on aggregate in their first qualifying round tie.
HJK could pose a real challenge to Malmo in the all-Nordic second qualifying round tie with the first leg taking place in Sweden next Wednesday.
Former Motherwell forward Henrik Ojamaa is part of the Estonian champions’ squad which comfortably overcame Hibernians of Malta 5-0 on aggregate in the first qualifying round.
Flora, whose domestic season began in April, will now hope to catch Legia Warsaw cold in the second qualifying round next week.
The Armenian champions needed extra time to beat Connah’s Quay Nomads of Wales 3-2 on aggregate on Wednesday night and now face Sheriff Tiraspol, the lowest ranked of the seeded clubs in the second qualifying round.
Alashkert have twice faced Scottish opponents in Europe - beating St Johnstone in the first qualifying round of the Europa League in 2015 and then losing to Celtic in the first qualifying round of the Champions League three years later.
Lincoln Red Imps
Beaten 5-0 by Rangers in the second qualifying round of the Europa League last season, Lincoln Red Imps’ most famous achievement remains their shock 1-0 first leg win over Brendan Rodgers’ Celtic before losing a Champions League second round qualifier 3-1 on aggregate in 2016.
The Gibraltarians enjoyed a comprehensive 7-2 aggregate win over Fola Esch of Luxembourg in the first qualifying round but are likely to find it much tougher next week against Cluj.