In their first-ever European quarter-final, Freiburg delivered a performance full of confidence and control under Julian Schuster. They set the tone early and never allowed the visitors to settle.
The breakthrough came after just 10 minutes. Captain Vincenzo Grifo cut in from the left and curled an effort into the far corner. The shot took a slight deflection, leaving goalkeeper Ionuà Radu with no chance.
Freiburg stayed aggressive instead of sitting back. Their high pressing paid off again in the 32nd minute when Philipp Treu won possession high up the pitch. Igor Matanovic kept his composure and squared the ball for Niklas Beste, who tapped in from close range.
The hosts nearly added a third before the break, with Johan Manzambi striking the post after a strong run, as Freiburg went into half-time firmly in control.
Celta boss Claudio Giraldez made changes at the break, but his side struggled to shift the momentum. Freiburg remained organised and disciplined, limiting the Spanish side to few clear chances. Former Bayer Leverkusen striker Borja Iglesias came closest, firing narrowly over from distance in the second half.
The third goal arrived from a set-piece. Beste's corner found Matthias Ginter, who powered home a header to seal a dominant night.
Speaking after the match, Grifo praised his side's approach: "We produced an incredible performance, very mature and very brave. We made good decisions, used the ball well and then the chances came."
He added: "From the first minute, we were clearly the better team. We wanted the third goal because we know it will be difficult in Vigo."
With a three-goal advantage, Freiburg head into the second leg in Spain firmly in control, but aware the job is not yet finished.