Argentine striker Pablo Osvaldo, fresh from a 90th-minute winner at Juventus on Sunday, lashed in an early shot that Joseph Yobo did well to block.
Left-back Manuel Pasqual was causing the visitors problems with his surges forward and twice his crosses found Fiorentina players, first Osvaldo heading at Howard, before Martin Jorgensen flicked a shot straight at the keeper.
Everton were struggling to string a handful of passes together and Yakubu - with eight goals in his last six games - was badly isolated up front.
They were becoming frustrated too, with Lee Carsley and Tim Cahill both fortunate not to be cautioned for poorly-timed challenges.
Just before the break Howard kept them level, his right leg somehow deflecting Vieri's fierce left-foot close-range shot wide when he seemed certain to score.
Montolivo (left) struck a late goal to hurt Everton's Uefa Cup hopes
If Everton boss David Moyes impressed on his side during the interval the need to improve their ball retention, his plea fell on deaf ears.
Even the introduction of Mikel Arteta for Leon Osman after 55 minutes failed to stop Fiorentina's momentum and twice in quick succession they nearly went ahead.
Vieri twisted and turned past Phil Jagielka and forced Howard to parry his thumping shot, before Yobo gave the ball away and Kuzmanovic hammered it in from 20 yards, the Everton keeper flying away to his left to make an athletic save.
Halfway through the second half Vieri was withdrawn for Giampaolo Pazzini, and soon after the home side got a goal their dominance deserved.
Montolivo's shot was blocked, the ball fell to Tomas Ujfalusi just inside the box and he teed it up for Kuzmanovic, who exquisitely side-footed into the corner from 20 yards.
Pazzini should have made it 2-0 when he badly miscued a volley from eight yards after a fabulous cross from substitute Massimo Gobbi picked him out.
But soon after Mario Alberto Santana sent in a ball from the right, Jorgensen deliciously flicked it up into Montolivo's path and the 23-year-old rifled in a sweet volley from 15 yards.
It was the least Cesare Prandelli's side deserved for a performance of genuine quality.
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