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).
Eriksen's perfect return
Eriksen was fitted with an implanted cardioverter-defibrillator (ICD) - a type of pacemaker - after his cardiac arrest against Finland during Euro 2020 nine months ago.
He joined Brentford on a six-month deal after his release by Inter Milan, who agreed to cancel his contract in December because players who have ICDs cannot compete in Serie A.
The Premier League does not the same regulations, and the Dane and made his first appearance for the Bees as a substitute in a defeat by Newcastle on 26 February.
The former Tottenham midfielder was given a standing ovation from fans and players on both sides when he came on after 52 minutes.
He said afterwards: "If you take away the result, I'm one happy man. To go through what I've been through, being back is a wonderful feeling."
Eriksen played the full game for Brentford in wins against Norwich City and Burnley before receiving his Denmark recall.
The Danes qualified for the 2022 World Cup in Qatar by finishing top of their group with 27 points from 10 games - four points clear of runners-up Scotland.
And Eriksen will hope to be part of the squad heading to the World Cup after capping his first game back with a sensational goal - and a man of the match award.
"I am looking forward to playing in Qatar but there is a lot of games in between," he added.