The Quarter Final draw paired Rangers with Italian outfit Torino.
Rangers had never faired well against Italian opposition. Defeats against Fiorentina in the 1961 European Cup Winners Cup Final and further defeats against both Milan clubs contributed to a poor record against the Italian teams.
In Italy, as opposed to what they had experienced in Portugal, their travel and pre-match arrangements were excellent. The players relaxed the evening before the game, by going to the stadium Torino shared with Juventus, to see the latter take on English side Wolves in a UEFA Cup tie.
The next evening's match in Turin's Stadio Communale, was watched by 35,000 spectators including many Rangers fans who had made the trip to the Northern Italian city.
Waddell deployed Derek Johnstone in defence to partner Colin Jackson, their job, to tightly mark the Torino danger men, Bui and Pulici. Dave Smith slotted in behind in the sweeper role.
Although it was a defensive system designed to frustrate the Italians, Rangers were still dangerous on the break and scored on twelve minutes through Willie Johnston after the Torino goalkeeper had dropped a Willie Mathieson shot.
In the second half Torino came back into the game and started to play with Italian flair. They put the Rangers goal under tremendous pressure and equalised on sixty-four minutes when Pulici got his toe to a Giovanni Toschi shot and turned it past Peter McCloy into the net.
In the last ten minutes the Italians tired, but the superior fitness of the Rangers players shone through. Torino resorted to "dirty tactics" with several punches thrown as their frustration grew.
The match finished 1-1. It was another undefeated away trip with the added bonus of an away goal.
Second Leg - 22nd March 1972
In the return leg, Torino knew they would have to score to have any chance of going through. Waddell's tactics for the home leg were similar to the first game, but Rangers had more freedom to break forward into attack. Torino's tactics were to lure Rangers into attack, win possession and then hit Rangers on the counter attack. The Italian team did not pose a lot of threat up front, but did in fact hit the post four minutes before the interval, but after forty-five minutes the score was 0-0.
Fifty-five seconds into the second half Rangers scored. Tommy McLean raced down the right and crossed the ball which was missed by both Torino 'keeper Castellini and Willie Johnston, but Alex MacDonald was at the back post to force it home.
Later on Willie Johnston hit the post and a Derek Johnstone header was cleared off the line, but when the final whistle sounded the score remained 1-0.
75,000 fans in the Ibrox stands and terraces voiced their approval as Rangers were through to the Semi-Final.