The Belgium international's harsh-looking sending off paved the way for the Polish champions to secure their first Group K points, with David Biton striking the all-important goal at Stadion Miejski on Thursday night.
Wisla were fortunate not to lose a man themselves in the opening two minutes after Ivica Iliev planted his foot in Brede Hangeland's chest.
Fulham's feeling of injustice was strengthened just before the half-hour mark when Dembele was harshly sent off for a push on Gervasio Nunez.
The man advantage gave Wisla the emphasis and, after a 13-minute delay to the second period due to a power failure, Biton's 22-yard effort condemned Fulham to defeat on their 20th competitive match of the season.
The visitors' disappointment was compounded shortly before the Israeli's goal when target man Orlando Sa hobbled off with what looked to be a hamstring injury, before Wisla's Osman Chavez was sent off late on.
Martin Jol made six changes from the side that lost 2-0 at Stoke and his team were unlucky not to see Wisla reduced to 10 men within the opening two minutes.
With the ball seemingly going nowhere, Iliev planted his foot in Hangeland's chest in a challenge akin to that made by Nigel de Jong in the 2010 World Cup final.
The former Partizan winger only received a booking for the challenge, which was followed by a further two Wisla fouls within a minute.
Fulham did not seem to be rattled by the early challenges and Damien Duff stung the palms of Sergei Pareiko in the fifth minute.
Iliev struck a cross-shot that Mark Schwarzer held with ease at the other end, before the dangerous-looking winger hit the crossbar.
The 31-year-old was given time to run through the heart of the field and unleashed a speculative 25-yard drive that rebounded off Hangeland and looped over Schwarzer onto the bar.
The White Star continued to impress as they attacked the raucous North Stand, with Schwarzer forced to save another Iliev drive in the 20th minute.
Fulham began to come forward with more purpose as the half progressed, with Dembele almost capitalising on some incisive passing only for Pareiko to save his curling effort.
Iliev again came close for Wisla moments later with a close-range drive, before Fulham received a controversial red card.
During an innocuous passage of play, Dembele was caught on the back of the ankle by Nunez and immediately pushed him to the floor.
The Argentinian midfielder went down clutching his face despite being pushed at shoulder height, leading referee Martin Hansson to hand the Belgium international a straight red card.
Fulham looked rattled by the decision and were penned in their own half for the remainder of the first period.
The start to the second period was delayed by 13 minutes after a power failure in the south-east corner of Stadion Miejski.
When play finally resumed, Fulham looked livelier although Schwarzer had to be alert to thwart an audacious 35-yard effort from Wisla skipper Cezary Wilk.
Then the match begun to swing in Wisla's favour, as target man Orlando Sa pulled up with what looked to be a hamstring injury and had to be replaced by Pajtim Kasami in the 58th minute.
The Cottagers' evening got even worse in the 60th minute when Biton picked up the ball in the middle and went on to break the deadlock, unleashing an unstoppable effort from 22 yards.
Wisla continued to press for a second and, after Andraz Kirm twice came close, Nunez fired a long-range effort straight at Schwarzer.
While only 16,577 were in the stadium, the home support were making themselves heard and would have had another goal to celebrate if Biton had not skewed wide.
The game became stretched as 10-man Fulham searched for an equaliser and Wisla defended in numbers.
Jol's side were given a glimmer of hope with three minutes remaining as Chavez received a second yellow card for a late challenge on Johnson.
However, the home side held out to secure a maiden victory against English opponents at the fourth attempt.