Three-time former champions Spain strolled past the Faroe Islands 4-1 and Ukraine hammered struggling Serbia 5-0 in Friday's Euro 2020 qualifying fixtures.
Republic of Ireland's James McClean said pre-match criticism of his team-mates by Denmark players served as motivation as they claimed a 1-1 draw in Copenhagen.
"Their players weren't complimentary towards us in the build-up to the game. We wanted to prove a point," McClean said.
Spain captain Sergio Ramos opened the scoring after six minutes before Jesus Navas doubled the lead just before the 20-minute mark.
Klaemint Olsen headed in from a corner after half an hour but the 102nd ranked side in the world's hopes of a surprise comeback were diminished four minutes later by a Teitur Gestsson own goal.
The Spaniards made sure of the three points and remained unbeaten at the top of Group F with defender Jose Gaya's first international goal with 14 minutes to play.
Sweden beat Malta 3-0 to retain second spot.
In Group D, Ireland's McClean criticised the Danish players' criticism of his team's playing style after a draw which left the visitors in pole position.
"It's not nice when professionals criticise you. Fair enough they beat us 5-1 but we've drawn the other four games we've played recently," he said.
"They're not that much better than us themselves, are they?," he added.
Christian Eriksen orchestrated Denmark's play in his first match since his club Tottenham were beaten in the Champions League final by Liverpool last weekend.
Elsewhere Ukraine humiliated Serbia in Lviv to leave the visitors, who qualified for the 2018 World Cup in Russia, rooted to the bottom of the group without a win in their opening three matches.
Schalke's Evgen Konoplyanka scored twice as the Ukrainians stayed top of Group B and five points ahead of reigning European champions Portugal who have played a game fewer.
Poland also continued their unbeaten start as they squeezed past North Macedonia 1-0 thanks to Krzysztof Piatek's second-half effort.