Kenny Miller scored the only goal as Rangers beat Progres Niederkorn 1-0 in the first leg of their Europa League qualifier on Thursday evening.
Niko Kranjcar set up the former Scotland striker after 37 minutes and he gave Pedro Caixinha's men a narrow advantage to take to Luxembourg on Tuesday.
St Johnstone were beaten 2-1 by FK Trakai at McDiarmid Park, with all the goals coming in the first half. Joe Shaughnessy netted for Tommy Wright's side, who travel to Lithuania for the return match on Thursday.
