Moore's 74th-minute goal cancelled out Breel Embolo's opener to earn the Dragons a valuable point in Group A.
Both teams showed intent from the first minute. However, no side was able to score in the opening half.
Embolo finally broke the Welsh resistance on 49 minutes with a powerful downward header after pulling away from his marker. It was his sixth international goal as Switzerland went ahead in the match.
But Wales struck back in the 74th minute as Moore's terrific movement created space to capitalise by glancing in from Joe Morrell's pinpoint cross.
Wales will next lock horns with Turkey on Wednesday while Switzerland will face Italy on the same day.
Baku [Azerbaijan], June 12
Kieffer Moore was the star of the day as Wales played out a 1-1 draw against Switzerland in their Euro Cup 2020 opening match on Saturday.
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