Fulham were outclassed in a one-sided opening half as Stead - a £750,000 signing from Sunderland - and midfielder Michael Tonge found the target.
Chris Coleman's side were pulled apart and when they rallied briefly after the interval, the Sheffield side held firm before Rob Hulse went close twice in the dying minutes.
United almost snatched a shock lead after just 30 seconds when Colin Kazim-Richards pumped a teasing cross into the goalmouth.
Leading scorer Hulse pounced as Antti Niemi dived at his feet, but the ball flashed over the target leaving the Fulham keeper needing treatment.
Niemi saved the London side minutes later as United sliced through his defence.
Stead threaded the ball to midfielder Stephen Quinn who ran through and poked the ball to the keeper's left as he charged off his line but it rolled a fraction wide of the far post.
Full-back Liam Rosenior slammed a shot from 20 yards high over the target and then cleared a dangerous Kazim-Richards cross from under the nose of Stephen Quinn as United turned the screw.
Fulham collapsed in the 23rd minute when Stead burst into the box to and blasted the ball into the roof of the net from close range for his first goal since signing from Sunderland.
United grabbed the second in the 28th minute with the lively Stephen Quinn again involved.
The little Irishman chased a loose ball and hooked it back into the goalmouth where the unfortunate Ian Pearce only half cleared and Tonge applied the finishing touch.
Stead had a long-range strike snatched on the line by Niemi before the Fulham keeper foiled the big striker by bravely diving at his feet after Chris Lucketti had headed a Kazim-Richards corner back into the goalmouth.
Fulham forced their way into the game but found the United back four well marshalled by skipper Phil Jagielka.
Hulse fired narrowly wide under pressure from Zat Knight and hit the bar seconds from time after beating Pearce eight yards from goal.