An incredible one-handed save from Mike Penders in the seventh minute stopped Alemão from giving Rayo the lead, before Jorge de Frutos fired over for the visitors when well placed.
By contrast, Strasbourg had managed just two touches in Rayo’s penalty area by the midway point of the first half, and were struggling to get their game going, with the creativity of Valentin Barco and the wing play of Julio Enciso completely nullified.
Penders had to be on his toes again as Unai Lopez let fly from range, and the LaLiga outfit continued to pile on the pressure until they got their reward in the 42nd minute.
Penders’ magnificent save from Florian Lejeune’s cushioned right-foot volley fell right at the feet of Alemao, and he gave Rayo the lead on the night.
Guela Doue's shot on target directly after was the hosts’ first, and unless they improved upon that output, it was going to be a long night for them.
If Strasbourg thought the second half would bring some respite, they were sorely mistaken, and they needed Penders’ acrobatics, again, to keep out Isi Palazon’s searing drive. It was difficult to see how the hosts were going to get back into the game, given that it was Rayo setting the tempo and, with 19 shots to Strasbourg’s three, the visitors were well on top in just about every aspect.
Martial Godo was the one shining light for the hosts as his five tackles were more than any other player from either side. That would have been little consolation to the Ligue 1 outfit, however, as an injury-time penalty from Enciso that was dramatically saved by Augusto Batalla, summed up their evening.
The result means Strasbourg have now lost five of their last six games in all competitions, and sees them bow out of the European competition not long after being dumped out of the Coupe de France. Rayo, meanwhile, are now unbeaten in five competitive games (W4, D1), and are deservedly in the final of this competition where they will meet Crystal Palace in Leipzig.