The 31-year-old opened his account in style with a deft backheel flick on 50 minutes, then a bullet header 12 minutes later to twice equalise at the Stade de Lyon.
The Real Madrid ace became the first player to score at four European championship finals and his 17th match in a Euro tournament was also a record.
The result left Hungary on top of Group F. Portugal squeezed through as one of the best third-place finishers but now face a tough match against Croatia.
It was his 128th appearance for Portugal, further extending the record he set last Saturday, as he made a record 17th appearance at Euro finals.
“These are just more records, but like I always say that comes naturally,” he said.
“I can’t say I’m not happy, these are good records, but the priority was to make it through to the 16.”