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.
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.
"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."
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.
