The victory could prove crucial for further advancement as Denmark and India are set to fight for second place in their group, while China is expected to win the group.
Earlier in the day, China won 5-0 in their match against Ukraine. The two best teams in the group advance to the quarter-finals.
Line Christophersen, the World No 21, was the first Dane in action. She lost in three sets to Pusarla Venkata Sindhu, India's best singles player.
Line Kjaersfeldt then restored parity with a two-set victory over Unnati Hooda, the World No 23. Denmark subsequently took the lead after the doubles team of Mette Werge and Amalie Cecilie Kudsk survived a match point.
The pair won in three sets over Shruti Mishra and Priya Konjengbam, a relatively unknown duo in an international context.
In the subsequent singles match, Amalie Schulz had the opportunity to decide the outcome in Denmark's favor - and she seized that chance.
Schulz lost the first set to the 17-year-old Tanvi Sharma, but she fought back and took the decisive victory.
Denmark's current best women's singles player, Mia Blichfeldt, was surprisingly not included in the team as she has been struggling with knee problems.