All I know is that until 1965, a decider was required if 2 teams remained draw after the home and away matches.
As by Fillet's comment: There were 2 matches in the 67-68 Cup winners cup quarter finals that went first to Extra Time, then to replay according to Wikipedia.
The first occurrence I came across was a second round Europa Cup I game in 73-74 between CSKA Sofia and Ajax, that was decided in ET. Going to check other cups too
Some background Extra Time after a tie did co-exist with a replay.
It seems, for UEFA competitions, that it first occurred in the 1957/58 Europacup I final between Real Madrid and AC Milan. But that was a one-legged match.
It only applied to the final. In previous rounds (double-legged) a third game was played.
In 1969/70 the third game was abandoned and replaced by away goals and a toss if still tied. But away goals only applied for first two rounds (which was already in place for the third game).
In 1970/71 the penalty shoot out was introduced in favor of the unfair coin toss. Away goals applied in all rounds.
I believe the extra time was
introduced in European football by fifa in 2004. Re-introduced by fifa in 2004
LAW 7 - The Duration of the Match
Extra Time Competition rules may provide for two further equal periods to be played. The conditions of Law 8 will apply.
Even though I think this was a rule that got change with the implementation of sudden death and the golden goal around 1999. Which People complained about because of the amount of pressure on the length of the match that suddenly ended if a goal was scored. Hence in 2004 the extra time was restored.(well I think)