Villarreal have found themselves on the end of a 3-2 defeat away at FC Zurich, courtesy of a frantic first half which saw all five goals scored in the first half-hour.
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Tomas Pina opened the scoring for the visitors in the 19th minute, but Franck Etoundi equalised two minutes later.
Gerard Moreno then fired the Yellow Submarine into the lead again in the 24th minute, but Berat Djimsiti and Yassine Chikhaoui turned the game around for the Swiss outfit.
Also in Group A, Borussia Monchengladbach secured a 2-0 win away at Apollon Limassol, though they were made to work hard for it, with both goals not coming until the second half.
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In Group B, Copenhagen succumbed to a 4-0 thrashing at the hands of Club Brugge, as Lior Refaelov bagged a hat-trick, while HJK of Helsinki shocked Serie A outfit Torino with a 2-1 win in Finland.
Tottenham Hotspur secured victory away at Asteras Tripolis, with an Andros Townsend penalty and a goal by the prolific Harry Kane earning Mauricio Pochettino's charges all three points in a 2-1 win in Greece.
Elsewhere in Group C, former Chelsea striker Demba Ba, also in good scoring form, bagged a brace to help Besiktas beat Partizan Belgrade 2-1.
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In Group D, Astra Giurgiu and Celtic played out a 1-1 draw, while Red Bull Salzburg thrashed Dinamo Zagreb 5-1 in Croatia, Jonathan Soriano's hat-trick setting the Austrians well on their way.
Dutch giants PSV Eindhoven secured an emphatic 3-2 win away at Panathinaikos in Group E, while Dynamo Moscow needed a second-half Kevin Kuranyi goal to beat Estoril Praia 1-0 in Russia.
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Finally, Group F saw Inter Milan scrape a 1-1 draw away at Saint-Etienne, while Qarabag FK succumbed to a 2-1 defeat at home to Dnipro Dnipropetrovsk.
Results in full: Apollon Limassol 0-2 Borussia Monchengladbach, FC Zurich 3-2 Villarreal, Copenhagen 0-4 Club Brugge, HJK 2-1 Torino, Asteras Tripolis 1-2 Tottenham Hotspur, Besiktas 2-1 Partizan, Astra Giurgiu 1-1 Celtic, Dinamo Zagreb 1-5 Red Bull Salzburg, Dynamo Moscow 1-0 Estoril Praia, Panathinaikos 2-3 PSV Eindhoven, Qarabag FK 1-2 Dnipro Dnipropetrovsk, Saint-Etienne 1-1 Inter Milan
