Inter take all three points and climb to the top of Serie A. Following a bright start, Barella gave Inter the lead just after the half-hour mark with a perfectly-placed strike from range.
The Nerazzurri increased their advantage seven minutes into the second half through Perisic, before Lukaku had a third called off for offside.
Fiorentina pushed to get back into the game in the closing stages, but Inter held on to claim all the points.
Fiorentina takes a trip to Sampdoria next time out in Serie A and will be looking to bounce back.
Inter meanwhile, host Lazio after their second leg semi-final tie in the Coppa Italia with Juventus.
The result was the perfect reaction from Inter after losing to Juventus in the Coppa Italia semi-final first leg tie on Tuesday.
Regardless, Inter saw out the win with comfort to reach 47 points, one ahead of rivals AC Milan who host Crotone on Sunday. Fiorentina stay 12th on 22 points.
The Nerazzurri got themselves in front in the 31st minute, with Barella curling an incredible strike into the net.
A stunning double save from Inter goalkeeper Samir Handanovic kept his side in front at the end of the first half, and those stops proved vital as the visitors increased their advantage seven minutes after the interval through Perisic.
Winger Achraf Hakimi cut inside from the right to find his left-wing partner Perisic in the area, who took Hakimi’s pass and fired it into the far corner.
With Antonio Conte serving a suspension from the touchline following his outburst away to Udinese, Cristian Stellini held the fort in Inter’s technical area.
But when asked in the aftermath of this triumph whether there was extra satisfaction in pressing more pressure on rivals AC Milan, the assistant coach was unmoved.
‘We don’t want to put tension on anyone, just thinking about our path,’ Stellini told Sky Sport Italia.
‘It was not easy to play in Florence just three days after our last match.
‘Games like these are always difficult, mainly with two days of recovery.
‘I’m pleased, we created a lot of chances and our forwards worked well together.’