Montella had laid the foundation for a fine comeback, which was capped by Routledge's injury-time winner.
BBC: SPORT | Football | My Club | Fulham | Montella has lift-off at Fulham
With Fulham struggling to create any meaningful chances, their manager Chris Coleman introduced Montella and Collins John.
The Republic of Ireland star was also involved in Montella's sending off after the former Roma striker raised his arm.
Montella's men controlled the game, created chances, hit the woodwork twice, but capitulated to a late header against the run of play.
WSJ: Mortella's Approach Paying Off for Italian Soccer's Fiorentina
Nine months after arriving in Florence, Montella is beginning to take off.
WSJ: Mortella's Approach Paying Off for Italian Soccer's Fiorentina
Having already turned and snapped a shot on to the woodwork, Montella was on hand to tap in a cross from Michael Brown.
BBC: SPORT | Football | My Club | Fulham | Montella has lift-off at Fulham
Montella says he doesn't play that way because of some philosophical dogma, but simply because he thinks it works and it's entertaining to watch.
WSJ: Mortella's Approach Paying Off for Italian Soccer's Fiorentina
Montella and Fiorentina have earned plenty of plaudits this season, precisely because so much of what they've done has been both counterintuitive and effective.
WSJ: Mortella's Approach Paying Off for Italian Soccer's Fiorentina
The referee was extremely lenient throughout, but he eventually brandished a yellow card at Leeds skipper Lucas Radebe for a dangerous tackle on Vincenzo Montella.
And should that dream come true, Montella is convinced that he can be part of an Azzurri side that can go on to achieve great things.
Montella, who had scored three goals in his previous two FA Cup games, immediately proved more adept at holding the ball and bringing other players into the match.
"Chance and probability are part of the game, " Montella says.
WSJ: Mortella's Approach Paying Off for Italian Soccer's Fiorentina
This was not the home debut of dreams and Montella was flapping his arms on the halfway line in frustration at the goal conceded by his new team-mates.
BBC: SPORT | Football | My Club | Fulham | Montella has lift-off at Fulham
Fulham also sent on Vincenzo Montella in a bid to add firepower, and he should have done better than fire wildly over from Brian McBride's cross after 64 minutes.
Trapattoni has had his squad settled for a while and it seems certain that 27-year-old Montella has done enough to force himself onto the plane to the Far East.
Montella also reveals that he was once a target for current England manager Sven-Goran Eriksson who had hoped to pair him alongside Christian Vieri when he was in charge of Lazio.
This week one Italian-based British reporter amused his counterparts by launching himself from the disco stage to steam around the dance floor, arms outstretched, imitating the goalscoring celebrations of Vincenzo Montella.
"We had a limited transfer budget, these were guys who were very good players who we could get at a discount because they weren't coming off stellar seasons or had been injured, " Montella says.
WSJ: Mortella's Approach Paying Off for Italian Soccer's Fiorentina
Going into the final quarter-of-an-hour, the Italian side exploded into life again with three good shots in the space of four minutes, for Totti, Delvecchio and Montella, kept out by a combination of Martyn's brilliance and luck once again.
应用推荐