Although Gary Madine's 50th-minute penalty was all that separated the sides, it was no fluke win by the Owls, who have started their Championship campaign brightly following promotion from League One last season.
Fulham, with seven Premier League goals in their opening two games this season, managed just one effort on target throughout the 90 minutes as they limped out of the competition.
The two sides had been involved in six games between them to date that had produced 30 goals but the first half was goalless, and the opening half-hour particularly nondescript.
In the closing 15 minutes, however, Wednesday visibly grew in confidence, perhaps realising on the evidence of those initial 30 that Fulham did not have much to offer.
Despite the changes made by Martin Jol, five initially on the team sheet but reduced to four just prior to kick-off when Damien Duff was a late replacement for Bryan Ruiz, on show was a strong Fulham side.
There was still no Clint Dempsey, seemingly an outcast given his hankering for a move to Liverpool, and more intriguingly Moussa Dembele was not part of the 18.
Jol appears to face a fight to hang on to the Belgian midfielder before the transfer window closes on Friday, with London rivals Spurs heavily linked of late.
But all Fulham had to show for their first-half efforts were long-range shots from Pajtim Kasami, Matthew Briggs and Steve Sidwell that were all comfortably off target.
Kasami and Sidwell also found themselves in referee Paul Tierney's notebook for fouls on Wednesday captain Jose Semedo and Giles Coke respectively.
Arguably, Sidwell was fortunate to avoid a second caution for a similar challenge on Semedo just beyond the half-hour, instead incurring a stern talking-to from Tierney.
After that the Owls finished the half the stronger, with Michail Antonio's direct running causing a fright.
His initial 36th-minute effort saw him disposses Alex Kacaniklic and embark on a surge towards the area, culminating in a rasping drive that forced Mark Schwarzer into a low save to his right.
After Schwarzer was relieved to see a free header from six yards from Madine fall safely into his grasp, Antonio had another opportunity in the 44th minute.
Played in by Chris Maguire, his run into the area on this occasion saw him cut back on to his left foot to leave with him a clear sight of goal, only to flash his shot just over the crossbar.
In the minute of added time Schwarzer then showed his alertness by plucking the ball off Madine's toes in the six-yard box from a piercing low cross from Chris Maguire.
Building on their strong end to the first half, Wednesday edged in front five minutes into the second from the spot.
Tierney had ignored penalty shouts just three minutes earlier when Aaron Hughes appeared to get a hand on a dangerous low corner from Maguire, steering it goalwards where Stephen Kelly cleared off the line.
Perhaps unsighted on that occasion given the crowded nature of the penalty area, Tierney then had a clear view of Kelly's foul on Maguire in the 49th minute, allowing Madine to send Schwarzer the wrong way for his first goal of the season.
The goal naturally brought a response from Fulham who did have the ball in the net in the 63rd minute, only for skipper Brede Hangeland to be ruled offside in heading home a Briggs cross.
Goalkeeper Stephen Bywater's one moment of action then saw him save a glancing Briggs header, but other than that he was untroubled such was the bluntness of Fulham's attack.
Instead, in the 77th minute, it was the home side who came within a whisker of doubling their advantage, only for Schwarzer to brilliantly tip on to the bar a sweeping 22-yard shot from Nejc Pecnik.Despite four minutes of added time, Fulham still could not find a way through Wednesday who deservedly take their place in the third round.
|Team Name||Sheffield Wednesday||Fulham|
|Shots On Target||4||0|
|Shots Off Target||3||3|