The victory lifted the Danes up into second spot in Group H - two points adrift of leaders Finland in Euro 2024 qualifying.
Tottenham midfielder Pierre-Emile Hojbjerg broke the deadlock for the Euro 2020 semi-finalists before Eriksen took centre stage.
The 31-year-old received the ball on the edge of the box and with his back to goal, pulled off a stunning backheel assist leaving Joakim Maehle to slot home Denmark's second of the match.
The assist was one of three on the night from the Red Devils maestro who also proved key in Jonas Wind and Yussuf Poulsen's goals.
His heroics on Thursday night took his tally to 39 strikes and 29 assists in 123 games for his country and United fans were quick to praise the efforts of their midfield star on social media.
Read more on Manchester United
Man United dealt another injury blow as new signing pulls out of international duty
Jadon Sancho stays at Man United despite late Saudi Arabia transfer interest
One fan said of his backheel: "What an assist."
Another posted: "If he plays higher up the pitch he's different class."
A third fan wrote: "He cooks for Denmark every single time because he's played in the correct position."
This supporter simply stated: "High IQ player."
Most read in Football
New Antony allegations, Lavia and Amrabat injury blows, Salah and Sancho stay
Hojlund roughing up Arsenal was great and aggression could ignite Man United's season
When Scotland can qualify for Euro 2024 with Tartan Army closing in on place in Germany
Ivan Toney in cryptic post as he trains alone for the first time since eight-month ban
Meanwhile this fan added: "Best Danish player in Manchester," in reference to his United teammate Rasmus Hojlund, who came on as a 59th substitute.
Hojlund made his debut for United in last weekend's 3-1 defeat at Arsenal and could be in line for his first start when the Red Devils entertain Brighton after the international break.
Eriksen hopes to retain his place in Erik ten Hag's starting eleven after coming off the bench in United's opening two games of the season.
He scored after being recalled for the 3-2 win over Nottingham Forest and started the disappointing defeat at the Emirates, assisting Marcus Rashford's opener.