Roy Hodgson's team earned a place in the Europe's second-tier competition last season and the West London club could repeat the trick this term if they can maintain their impressive form on home turf. Cottagers captain Danny Murphy opened the scoring and David Elm added a second for the hosts before half-time. Bobby Zamora wrapped up the points after the interval.
Brian Laws' visitors had claimed a crucial win over fellow strugglers West Ham on Saturday to climb out of the bottom three. But the Clarets are just two points above the relegation zone after another dismal away-day. Burnley were still looking for their first away win of the season and any belief that they could end that run here were dashed before half-time.
"I thought the victory lay in the hard work and the quality of our defending," said Hodgson. "We gave them very little time and space to play and we used the ball wisely. We got everything right tonight - the defending and attacking - and on a night like that, we would have been a tough nut to crack for any team."
Laws admitted it is vital that his side manage to break their away duck. "Psychologically it will start to affect the players," conceded Laws. "We have to change the mind set. We put in a magnificent performance against West Ham on Saturday and we have not had time to enjoy that because there was another important game against Fulham."
The Cottagers didn't have to wait long for the opening goal as Murphy broke the deadlock in the 23rd minute. On-loan Aston Villa defender Nicky Shorey crossed from the left and Elm, taking advantage of the linesman's debatable decision not to flag him offside, headed down for Murphy to stroke home from close-range.
Burnley briefly sparked into life when Steven Fletcher's fierce, angled drive skimmed past Australia goalkeeper Mark Schwarzer's far post. Dickson Etuhu came close to increasing Fulham's lead with a powerful long-range effort which Brian Jensen pushed away at full-stretch.
With Burnley creaking under the weight of Fulham's pressure it was no surprise that Elm put the hosts in complete control in the 31st minute. Zamora surged past Leon Cort and his shot parried by Jensen to Elm, who calmly slotted home his first goal for the club.
Laws responded by sending on Chris Eagles for Cort and Burnley almost got one back just before the break when defender Tyrone Mears hit the angle of crossbar and post with a superb free-kick. That close-shave proved a false dawn for Burnley. The visitors have taken just one point on their travels and Zamora ensured that would remain the case in the 54th minute.
Zamora was fouled by David Edgar on the edge of the Fulham penalty area and the former West Ham star picked himself up to curl a low free-kick past Jensen's weak attempted save. Substitute Stefano Okaka, on loan from Roma, twice went close to increasing Fulham's margin of victory in the closing stages but the damage had already been done.