Hertha Berlin, in last place in the Bundesliga, scraped through thanks to a 1-0 win at home to Group D winners Sporting and Panathinaikos of Greece secured second place in Group F when Djibril Cisse scored two in a 3-0 win over Dinamo Bucharest.
The biggest drama of the night came in Belgium, when Ivan Perisic netted the winner in added time to beat visiting Toulouse 1-0 and send Club Bruges through from Group J at the expense of the French side.
Werder Bremen scored three without reply at Athletic Bilbao to secure top spot in Group L, with the Basque club and the Germans already through, and FC Copenhagen coped better with the wintry conditions in Prague to defeat Sparta 3-0 and eliminate the Czechs from Group K.
Amid the snow flurries in Basel, Zamora swept in his first goal from Riise's centre after 41 minutes of the Group E clash and he doubled Fulham's lead four minutes later when he rose unmarked to nod in another fine cross from the Norwegian.
Alex Frei pulled back a goal for the home side from the penalty spot after Aaron Hughes handled in the area before Zoltan Gera netted Fulham's third on 77.
Marco Streller gave Basel hope when he headed home from a corner with three minutes remaining but Fulham held on.
ITALIANFANS ARRESTED
"It's not normal for Fulham to be in Europe, having qualified through our League position, so I'm really pleased for them and the players too," Fulham coach Roy Hodgson said on the club's website.
"Already we've done more than we perhaps set out to do, so it's been a bonus to get so far and it would be an even bigger bonus in the future," he added.
AS Roma topped the group on 13 points after Alessio Cerci's double and a goal from teenager Filippo Scardina gave the Italians a 3-0 success at eliminated CSKA Sofia. Fulham were second with 11 and Basel third on nine.
Bulgarian police arrested eight Italian fans before the match in Sofia after around 60 caused trouble in a bar and clashed with officers.
"They threw chairs, beer bottles and ashtrays at us and no doubt some of them were drunk," a police officer told Reuters. "They were very, very aggressive."
The top two from the 12 groups qualify for the knockout stages, where the third-placed teams from the eight Champions League groups will also feature.
In Thursday's matches, La Liga side Valencia have a two-point advantage at the top of Group B ahead of their match at Genoa, with the Italians and French club Lille, who host eliminated Slavia Prague, both on seven.
Juventus, Liverpool, Olympique Marseille, Atletico Madrid, VfL Wolfsburg, Rubin Kazan, Unirea Urziceni and Standard Liege are all joining from the Champions League and the draw for the last 32 is on Friday in Nyon, France.
Portuguese side Benfica, Galatasaray and Fenerbahce of Turkey, Austrian club Salzburg, Shakhtar Donetsk of Ukraine and Dutch side PS
