Danny Murphy's second-half goal separated the sides on the night, with the three points taking the unbeaten Cottagers to the top of Group E.
Manager Roy Hodgson again tinkered with his line-up in Europe after handing starts to Bjorn Helge Riise, Chris Smalling, Stephen Kelly, Chris Baird and Jonathan Greening.
Fulham's much-changed side could have found themselves a couple of goals down after a sometimes torrid first half.
Alexander Frei scuffed a 15th minute shot wide of the mark after being picked out by Behrang Safari.
Midfielder Benjamin Huggel struggled to hide his embarrassment midway through the first half when he was left unmarked at the back post but somehow blazed over the bar from close range when it looked easier to score.
In-between, Andrew Johnson pounced on a mistake by Serkan Sahin but drove a shot from 20 yards just wide of the upright.
Johnson was denied a penalty on the stroke of half-time when he went down in a heap after trying to round goalkeeper Franco Costanzo.
Fulham visibly upped the tempo at the start of the second period and Murphy finally broke the deadlock after 57 minutes.
Johnson picked out Murphy with a pinpoint cutback and the midfielder clipped a low curling shot into the far corner of the net from the edge of the penalty area.
The goal lifted Fulham and Johnson was left looking on in yet more bemusement when he was denied another penalty on 70 minutes following a challenge from the outstretched leg of Safari.
Basel's response was to make a couple of attacking substitutions and the visitors began to enjoy more possession.
Marco Streller hooked an eight-yard shot over the bar in the closing minutes when he should have done better, before substitute Antonio da Silva curled a 25-yard free-kick marginally wide of the upright.
Goalkeeper Mark Schwarzer then saved his side in stoppage-time with a fine one-handed save at full-stretch to deny Scott Chipperfield.
The result has left Fulham at the top of their table with a one-point advantage over Basel and group favourites AS Roma with two games remaining.