Despite having a three-goal deficit from the first leg, Celta surprisingly showed very little fight in the first half, and it was Freiburg who capitalised by putting the tie beyond any doubt.
The visitors showed their intentions from the start, as Johan Manzambi tried his luck from range but struck wide. Nevertheless, their next two efforts ended up in the back of the net, with the first one particularly spectacular.
A long ball fell to Jean-Victor Makengo to knock down, and Igor Matanovic did the rest as he produced a sumptuous volley into the top corner for his third UEL goal this term.
Yuito Suzuki then matched his tally before the break by playing a neat one-two with Jan-Niklas Beste prior to finding the bottom corner with the aid of a deflection off Marcos Alonso’s outstretched leg.
Freiburg had conceded a competition-low six goals before kick-off, and Celta needed to score as many in the second half alone to produce the comeback of all comebacks.
Instead, it was the Germans who filled their boots again to match the scoreline from the first leg, with Suzuki completing his brace.
Manzambi did well to dribble towards goal and almost rounded Ionut Radu, but the ball broke to Vincenzo Grifo, who laid off for Suzuki to place into the bottom corner.
Iago Aspas searched for his seventh UEL goal contribution this season (G3, A3) to at least give Celta a consolation, but his free-kick curled just wide.
Freiburg, meanwhile, were immediately dangerous down the other end, with two substitutes going close as Lucas Holer hit the post before Derry Scherhant saw his rebound expertly tipped wide by Radu.
For Celta, Fer Lopez flashed his effort inches past the post as his side were still unable to test Noah Atubolu. Jones El Abdellaoui did manage to do so a few minutes later, though, but Atubolu denied him from close range.
Although they did show a little more fight in the final stages, even finding the back of the net through Williot Swedberg in injury time, Celta were comfortably beaten as they conceded three goals for the third game in a row.
Freiburg’s defence, on the other hand, was only breached once throughout 180 minutes of this tie, and with just a second away victory in nine UEL matches (D3, L4), they sail safely through to the semi-finals of a UEFA competition for the first time in their history to go alongside their progression to the last four of the DFB-Pokal.