Among the first to congratulate Ronaldo was Daei who said on Instagram: "I am honoured that this remarkable achievement will belong to Ronaldo - great champion of football and caring humanist who inspires and impacts lives throughout the world."
The brace also gave Ronaldo sole possession of the record of most goals at Euros and World Cups with 21 strikes, breaking a tie with German World Cup top scorer Miroslav Klose who has 19.
Ronaldo is the record all-time scorer at the Euros with now 14 goals and the top scorer of the current tournament with five strikes.
Wednesday also saw him gain sole possession of the appearance record at the Euros, including qualifiers, with 59 games, one more than former Italy goalkeeper Gianluigi Buffon.
He also has the most matches at Euro finals with 24 and is the only player to have played at five Euros, making his debut in 2004.