- Tag results for Nations League
Eden Hazard converted a 29th-minute penalty after a foul on Lukaku, with the Manchester United striker netting a quick-fire second before adding a third in the closing stages.
Portugal was without Cristiano Ronaldo, who had been left out of the squad at his own request to focus on his new Italian club Juventus.
The Tottenham midfielder put the Danes ahead with just over half an hour gone in Aarhus. Eriksen then added a second on 63 minutes from the penalty spot after Ethan Ampadu handled.
Kane raged at Dutch referee Danny Makkelie for ruling out a late equaliser as Spain punctured England's post World Cup euphoria by winning 2-1 at Wembley to hand coach Luis Enrique a winning start.
Hosts Russia were one of the surprises of the summer's World Cup, when they came close to booking a place in the last four before exiting the competition 4-3 on penalties to Croatia.
Italy will seek to restore pride after their failure to reach this year's World Cup when they take on Cristiano Ronaldo's Portugal and Poland.