Dempsey followed up a stupendous side volley with a bundled effort at Craven Cottage, before Brede Hangeland added a third with a header.
The victory extended Fulham's unbeaten league run at Craven Cottage to seven matches, having last tasted defeat at the hands of London rivals West Ham on Boxing Day.
That result left last season's UEFA Europa League finalists facing a potential relegation battle but now they lie ninth in the Barclays Premier League table.
And having all but staved off relegation, Dempsey believes the only way is up. "I would like to think we could do what we did in the past," he said.
"That we could be fighting for Europe and push on from there. We got to see the way things go but I don't think [last season] was a fluke. I think we have the quality here and hopefully we can show that. I would like to think that [we are safe] but there are still four games left and you don't want to be waiting until the last game and stressing.
"I think we are trying to look up, we are trying to make sure we finish in the top half because we feel that we have the quality in our team that we should be a team in the top half. That is the main goal now in our four games left."