Following the contest "Après toi" became internationally a commercially successful Eurovision winners. Leandros recorded versions of the song in several languages and topped the charts in a number of European countries. Leandros took the English-language version of the song ("Come What May") to number 2 on the UK Singles Chart, at the time by far the highest position achieved in the UK by a non-British/Irish Eurovision winner.
On the night of the final Leandros performed 17th in the running order, following Belgium and preceding the Netherlands. Prior to the contest most observers had predicted a two-horse race between Luxembourg and the United Kingdom, with the Netherlands as the only other possible challenger. In the event, "Après toi" took the initiative in the first round of voting, and did not relinquish the lead throughout the whole voting procedure. The song won the contest with a score of 128 points, 14 points ahead of the United Kingdom's "Beg, Steal or Borrow".
The voting system introduced in 1971 – two jury members from each country awarding between 1 and 5 points to each song – was used again, despite its inherent flaws. Each country's pair of voters had a minimum of 34 and a maximum of 170 possible points to award, and there had been much criticism after the Luxembourgian pair in 1971 gave out only 42 points in total, awarding the minimum score of 2 to all but four of the other entries, and only deeming one song worthy of even 5 points out of 10. Perhaps in response to the criticism, the 1972 Luxembourgian pair proved exceptionally generous, handing out 107 points in total.