Andy Johnson came closest to breaking the deadlock for Fulham in the first half
Danny Murphy's second-half goal ended Fulham's run of three successive losses thanks to a table-topping Group E win over Basle in the Europa League.
The midfielder latched on to Andy Johnson's cutback in the 56th minute before unleashing a skidding 18-yard strike past goalkeeper Franco Costanzo.
Basle had good chances either side half time as Benjamin Huggel and Marco Streller fired over from close range.
And Mark Schwarzer's diving save denied Mark Chipperfield in the final minute.
The full-time whistle came at just the right time for the London side as Basle pushed forward relentlessly in search of an equaliser in the final 10 minutes.
Switzerland international striker Streller blazed over from eight yards following excellent work on the left from Valentin Stocker in the 83rd minute before substitute Antonio de Silva's superb curling 35-yard free-kick only just evaded Schwarzer's right-hand post.
Despite a nervous finale, Fulham held on for a confidence-boosting win ahead of an important Premier League match against fellow strugglers West Ham on Sunday.
Boss Roy Hodgson rested Brede Hangeland, bringing in teenager Chris Smalling, while John Pantsil, Aaron Hughes, Damien Duff and Dickson Etuhu, who all started in the 1-0 defeat by Arsenal last week, were missing.
Swiss team Basle, who beat Italian giants Roma in the previous round, boasted experienced strikers Alexander Frei and Streller up front.
And Frei was called into action in the 12th minute when Behrang Safari's strong found the Switzerland captain inside the box, but his weak 14-yard left-foot strike rolled harmlessly past Schwarzer's left post.
The visitors should have taken the lead in the 23rd minute when Streller's intelligent header found Huggel unmarked inside the six-yard box, but the midfielder sent his shot high over the crossbar.
Although Johnson had a penalty claim on the cusp of half time dismissed by German referee Michael Weiner, the striker was involved in the build-up for Fulham's goal 11 minutes after the interval.
After latching on to Stephen Kelly's pass, Johnson skipped away from two defenders before his accurate cutback was perfectly slotted past Costanzo's dive by Murphy from the edge of the 18-yard box.
The goal stiffened Basle's resolve, with manager Thorsten Fink withdrawing defender David Abraham in favour of the attacking invention of Antonio da Silva.
Substitute Chipperfield went close in injury time, but Basle could not find a way past Schwarzer as Fulham held on to move top of their group.
Fulham boss Roy Hodgson: "We were playing a good team, it was a very tough game. We were better in the second half, got on top and luckily scored our goal - but they made it tough to the final minutes.
"It was a gritty performance in terms of our defending - which is an important part of the game.
"We were able to rest one or two senior players, who I hope will recover for the weekend. It's important to use your squad in this competition."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.