Venuti left the field in tears after he deflected Juan Cuadrado's cross into his own net in the first minute of stoppage time to hand Juve the win and a potentially crucial away goal.
Serbia forward Vlahovic was back at the Stadio Artemio Franchi for the first time since moving to Turin in January but had little joy for depleted Juve in a tense match which lacked quality.
The tie will be decided at the Alianz Stadium next month, with the winners taking on either AC Milan or Inter Milan - who drew 0-0 on Tuesday - in May's final in Rome.
Fiorentina fans had promised a fiery welcome for former hero Vlahovic, whose departure to fierce rivals Juve for an initial 70 million euros brought an end to months of speculation around the 22-year-old's future.