And the Premier League side had looked in control until Nevland's red card at the Stadio Olimpico, before going on to lose.
Within seconds of his arrival on the pitch, debutant Duff crossed to fellow substitute Erik Nevland and his back header was buried by Zamora.
Roma boss Claudio Ranieri believed the red card for Nevland was a turning point in the game but a deserved punishment for the Fulham striker.
Fulham substitute Eric Nevland later saw his shot turned around the post while Pizarro's cross was sent just wide by Riise at Schwarzer's far post.
The Cottagers had Erik Nevland sent off by referee Kevin Blom when 1-0 up and went 2-1 down before Paul Konchesky was also dismissed late on.
Zoltan Gera took his place on the left, with Simon Davies making his first start of the season following an ankle injury at Erik Nevland's expense.
Nevland had only come on at the start of the second half before being dismissed four minutes later for a tackle on Roma midfielder Daniele de Rossi.
But Nevland was sent off for a 49th minute tackle on Daniele de Rossi before John Arne Riise equalised with a shot that deflected off two players.
Nevland had only been on the pitch for four minutes when he was sent back to the changing room for clipping De Rossi's heels with a sliding challenge.
An unmarked Kamara headed wide at the far post before Dempsey angled a shot wide after being set up by Gera and Nevland's red card then proved decisive.
Johnson, who broke his collarbone in the 3-1 first-leg win a week ago, was replaced by former Manchester United forward Erik Nevland who was deployed up front on his own.
Hodgson brought on Diomansy Kamara to replace Nevland on the hour and Fulham, at last, showed glimpses of creativity as Zoltan Gera, Dickson Etuhu and substitute Seol Ki-Hyeon had chances to score.
But it was the dismissal of Nevland that had changed the course of the game and, while Fulham had a measure of control beforehand, they were forced into a rearguard action after the dismissal.
But with Andy Johnson, Bobby Zamora, Erik Nevland and David Elm ahead of him in the pecking order at the Premier League club, he has opted to move to Glasgow for regular football with a manager he knows well.
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