Victory in the 1979 Scottish Cup Final over Hibernian required a second replay to separate the sides before Rangers eventually won 3–2.
The 1979 Scottish League Cup Final ended in a 2–1 win for Rangers over a strong Aberdeen with goals from Alex MacDonald and Colin Jackson.
Wallace's treble-winning team of the previous season performed well in the European Cup.
Rangers eliminated Juventus after defeating the Italians 2–1 on aggregate – the first time Rangers had ever recovered from a first-leg defeat to win a two-legged European tie.
Dutch side PSV Eindhoven, the then UEFA Cup holders, were overcome in the next round (the club's first home defeat in European competition), before an injury-stricken Rangers side lost to Cologne at the quarter-final stage.