Cristiano Ronaldo - Getty Images
Ronaldo's strike, which put the title holders 2-0 up with three minutes left, was his 10th in the European Championship finals, spread across five tournaments going back to 2004.
He beats the previous mark of nine set by France's Michel Platini.
It was an 87th-minute penalty after a foul on Rafa Silva meant which took him above Michel Platini for most European Championship goals scored, taking his tally to 10 after Raphael Guerreiro's deflected goal had given them the lead three minutes earlier.
Ronaldo, who missed a sitter in the first half, then delivered the final blow to a spirited Hungary side with a goal after a brilliant Portugal move in stoppage time.
Before Portugal's goal rush, Hungary thought they had snatched a first win over the visitors in their 14th meeting much to the delight of a packed stadium when Szabolcs Schon had the ball in the net. But the winger's effort was disallowed for offside in the build-up.
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