Jonas scored midway through the first half 0, on Thursday at the Mestalla to capture its 0.
Valencia won the first leg in England, 1-0, and Jonas put the Spanish squad in complete control when converted to the lower-left corner in the 25th minute in one of seven early matches.
Spanish side Athletic Bilbao joined Valencia in the last 16, as Muniain scored in the 62nd minute - 2 minutes after teammate Fernando Amorebieta was sent off - to give his side a 1-0 win and an away goals victory over Loko Moscow.
Loko Moscow won the first game in Moscow, 2-1, but the away goal put Bilbao in good position for the second leg at the San Mames, and Muniain's goal tied the series on aggregate and put his side through.
Dutch sides PSV Eindhoven and Twente also secured advancement, as PSV defeated Trabzonspor 4-1 for a 6-2 aggregate win, and Twente edged Steaua Bucharest 1-0 to wrap up its series on a 2-0 aggregate.
Tim Matavz scored a brace for PSV, while Nacer Chadli scored Twente's goal.
Italian side Udinese used goals from Danilo, Antonio Floro Flores and Maurizio Domizzi to win 3-0 at Greece's PAOK and advanced on the same aggregate score. Germany's Hannover used a goal from Mame Biram Diouf for a 1-0 victory over Belgium's Club Brugge, and a 3-1 aggregate win in the series.
Wisla Krakow, which had Gervasio Nunez sent off in the 64th, held on for a 0-0 home tie at Standard Liege, but the Belgian hosts advanced on away goals after a 1-1 deadlock in Poland in the first leg.