Valencia matched the competition's record win, while Danish minnows Midtjylland beat Manchester United and Borussia Dortmund and Sevilla racked up notable victories.
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Midtjylland pulled off the shock of the night, with Valencia – in record-equalling style – and Sevilla assuming notable round of 32 first-leg leads of their own.
Valencia are all but through to the last 16 after a sensational 6-0 defeat of Rapid Wien on coach Gary Neville's 41st birthday. The Liga side became the first team to score five in the first half of a UEFA Europa League fixture and added a sixth late in the second period. They match the biggest win in the history of the competition, set by Steaua Bucureşti against Aalborg last season.
Three-time European champions Manchester United, meanwhile, entering the competition having finished third in their UEFA Champions League group, were expected to be among the teams to beat in the knockout stage. Danish minnows Midtjylland, though, did just that, coming from a goal down to ensure they have a 2-1 advantage to take to Old Trafford next week.
Only two sides apart from Valencia have more than a one-goal lead to protect in the return legs, Borussia Dortmund (2-0) and Sevilla (3-0) winning at home against Porto and Molde respectively.
MATCHDAY FIVE RESULTS (click for match reports and video highlights)
Anderlecht 1-0 Olympiacos
Midtjylland 2-1 Manchester United
Fiorentina 1-1 Tottenham
Borussia Dortmund 2-0 Porto
Villarreal 1-0 Napoli
St-Étienne 3-2 Basel
Sevilla 3-0 Molde
Sporting CP 0-1 Leverkusen
Valencia 6-0 Rapid Wien
Augsburg 0-0 Liverpool
Sparta Praha 1-0 Krasnodar
Galatasaray 1-1 Lazio
Sion 1-2 Braga
Shakhtar Donetsk 0-0 Schalke
Marseille 0-1 Athletic
Fenerbahçe 2-0 Lokomotiv Moskva (Tuesday)