The substitute got Copenhagen’s third goal in the 90th minute after replacing Rasmus Falk in the 79th minute – thus becoming the club’s youngest scorer in the competition’s history.
Viktor Fischer gave the Danish team a dream start after 18 minutes thanks to Pierre Bengtsson’s assist, however, the lead was short-lived after Vladimirs Kamess’ equaliser.
Pieros Sotiriou’s 62nd-minute penalty placed Stale Solbakken’s side in front before Daramy’s strike ended the Latvians’ quest for a comeback.
Latvia’s Riga will welcome Copenhagen to Skonto Stadium for the return leg on August 29 as they chase a place in the Europa League group stage.
Daramy began his youth career at Hvidovre IF before signing his first professional contract with Copenhagen on April 2019.
He is expected to play a role when his club faces Nordsjælland in Sunday’s Superlig encounter. Solbakken’s men are leading the table with 18 points after six games.