Ianis Hagi had a penalty saved before Ryan Kent scored the only goal as Steven Gerrard's men defeated Braga 1-0 (4-2 on aggregate) to continue their fine form in Europe this season.
Rangers can now look forward to Friday's draw for the last 16 of the competition, with ties scheduled for March 12 & 19.
Celtic take on Copenhagen at Parkhead on Thursday, with the scores level at 1-1 after the first leg in Denmark last week.
