Eriksen, 30, was playing for his country for the first time since his cardiac arrest at Euro 2020 last June.
The midfielder, who has since joined Premier League club Brentford, produced a terrific finish into the top corner.
“I was happy the ball came to me,” said Eriksen.
“I thought it was a lovely finish and to start my international comeback like this is a perfect way.”
Eriksen could have had a second goal when he turned outside the area, but his curling strike hit a post.
Tottenham’s Steven Bergwijn did score twice for the Netherlands, with Nathan Ake and Memphis Depay also on the scoresheet, while Jannik Vestergaard netted Denmark’s first goal.
But it was Eriksen who was the centre of attention – coming on to win his 110th cap as a second-half substitute to huge cheers from the crowd at Johan Cruyff Arena in Amsterdam, home of his former club Ajax.
Netherlands manager Louis van Gaal was among those to clap Eriksen, who applauded in return.
And just two minutes later he sent his team-mates and fans into raptures, rattling home a confident finish from Andreas Skov Olsen’s cutback.
“It has always been lovely place and today is an even more special place for me to play my first international game in this stadium,” added Eriksen, despite someone throwing a coin towards him during his post-match interview.
Denmark next face Serbia in a friendly on Tuesday (17:00 BST).
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