Stansfield, 21, who was Birmingham's multiple player of the year and 13-goal top scorer last season, netted after 14 minutes after Raul Jimenez's 10th-minute penalty gave Fulham the lead.
Birmingham - who are set to sign QPR striker Lyndon Dykes for around £1.5million - hit the bar through Willum Willumsson's blistering free-kick.
But Fulham's Premier League quality shone despite 11 changes to their lineup. For League One hot favourites City, defeat ended their unbeaten four-match run.
The Londoners won a penalty with their first serious attack after a handball by City left-back Alex Cochrane. Former Wolves striker Jimenez kept his nerve to coolly roll the ball to the left of goalkeeper Ryan Allsop, who went the opposite way.
Birmingham's first chance came when Christoph Klarer's looping header was held under the bar by goalkeeper Steven Benda. But Fulham returned to the attack to double their lead through Stansfield.
The youngster refused to celebrate out of respect to the club where he spent last season and was applauded by the City fans behind the goal. Stansfield attempted to double his account with an audacious 40-yard effort but it drifted wide.
Keshi Anderson's header was nodded off the line by Timothy Castagne as City sought a way back into the tie.
But Fulham were in control and they almost snatched a third goal when Krystian Bielik put behind his own goal under pressure from Jimenez.
Birmingham went closest to opening their account in the first period two minutes before the break when Willumsson's thunderous free-kick crashed off the bar to safety.
Birmingham looked to take the game to Fulham after the break without threatening Fulham's goal. City manager Chris Davies made a triple substitution just after the hour to drag his side back into the tie.
Tyler Roberts, Koji Miyoshi and Ayumu Yokoyama replaced Alfie May, Emil Hansson and Anderson and it seemed to work as City threatened for the first time in the second half.
Cochrane let fly with a full-blooded drive but his 25-yard effort was pushed around the post by Benda. Stansfield was applauded by both sets of fans when he was substituted in the 78th minute.
Millwall fell to a shock 1-0 loss at home to London rivals Leyton Orient, while Watford overcame Wayne Rooney’s Plymouth 2-0 in an all-Championship contest at Vicarage Road.
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