|DELGADO'S KEY MATCH STATS|
Their last-16 tie with Red Bull Salzburg saw them go 1-0 behind in the second-leg and see a man sent off, after a 0-0 home opener.
Playing with 10 men did not stop the visitors to the Red Bull Arena causing an upset, however, as two second-half strikes stunned the Austrians and let Murat Yakin's men progress.
Faced with Valencia in the quarter-finals, Basel were once again expected to bow out but Delgado's double changed the face of the game with half-time around the corner.
The central midfielder - who was brought back to the club last summer after a seven-year absence - thumped home an effort on 34 minutes before scoring his second of the night shortly afterwards.
Delgado's goalscoring heroics came from absolutely nowhere. The Argentine, 31, has not scored once in competitive matches this season and has featured sporadically in their European campaign.
Valentin Stocker grabbed a stoppage-time goal, dinking into the back of the despairing Spanish side's net, to secure a brilliant 3-0 win for Basel.
The emphatic victory was made even more impressive because St Jakob Park was bereft of the usual home support. Crowd trouble in the previous home tie - which had brought the game to a temporary halt, such was the commotion from Basel's visiting fans in Salzburg - saw Uefa crackdown by demanding the opening leg of the last eight be played behind closed doors.
Ironically, they will actually have more fans at Mestalla in a week's time and, with los Che on life support, the likes of Delgado will be hoping to at least match last year's Europa League semi-final showing by preventing capitulation.