Chasing a record fourth triumph in Europe's second-tier club competition, Sevilla took the lead in the 17th minute at a festive Sanchez Pizjuan stadium when Vidal thrashed a low shot into the corner from a Carlos Bacca layoff.
The Spanish midfielder made it 2-0 to the Andalusians seven minutes into the second half when Vitolo released him into space on the right of the penalty area and he finished clinically past Fiorentina goalkeeper Neto.
Substitute Gameiro put the tie virtually beyond the Italians 15 minutes from time when he scored with his first touch just under 30 seconds after replacing Bacca following good work down the left from fullback Benoit Tremoulinos.
It was Sevilla's ninth win in a row at home in continental competition and their seventh in seven matches at the Sanchez Pizjuan in the latest edition of the Europa League.
"Fiorentina deserved to be here but we again demonstrated our strength at our stadium and got another positive result," Vidal told Spanish television.
"We cannot relax in the return because if they get into the game early on we could suffer," added the 25-year-old, who had never scored in nine previous European appearances.
"If we said that the tie was evenly balanced we would be lying. But I repeat that we cannot let our guard down because they could get a result like we got today."
Fiorentina's Serie A rivals Napoli squandered the lead and drew 1-1 at home to Ukrainian side Dnipro Dnipropetrovsk in their semi-final, first leg, with the return legs to be played in a week's time.
Sevilla won back-to-back UEFA Cups in 2006 and 2007 and can eclipse Inter Milan, Juventus and Liverpool, who each won the competition three times.
(Writing by Iain Rogers, editing by Toby Davis)
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