UEFA Europa League: Fiorentina 2 Dynamo Kiev 0
Fiorentina are aiming to qualify for their first European final in 25 years, having finished as UEFA Cup runners-up to Juventus in 1990, and remain on course following a first win in five matches in all competitions.
The Serie A outfit piled on the pressure in the early stages - Gomez seeing a goal disallowed for offside following a goalkeeping blunder, before Marcos Alonso found the crossbar.
Fiorentina were boosted when Jeremain Lens received his second booking for an alleged dive on the edge of the penalty area, although television replays suggested he may have had cause to feel hard done by.
That incident occurred five minutes before half-time, and Fiorentina wasted little time in taking advantage, with Gomez finding the net three minutes later.
Dynamo's threat was limited throughout, and, with the exception of a late Sergiy Rybalka effort, they showed little sign of forcing extra-time, or snatching victory, and Vargas wrapped up the win in the fourth minute of stoppage time.
Fiorentina, who made nine changes from their 1-0 Serie A defeat to Verona on Monday, looked dangerous early on and came close to opening the scoring when Gomez just failed to get on the end of a Joaquin cross after two minutes.
Gomez looked to have put the Italian side in front three minutes later when goalkeeper Oleksandr Shovkovsky clumsily spilled the ball into his path from a fierce Borja Valero strike for a simple tap-in, but the linesman's flag had already been raised for offside.
Shovkovsky redeemed himself somewhat when he got down well to keep out Mohamed Salah's low drive, but was unable to stop a Alonso strike that rattled the crossbar after 10 minutes.
Fiorentina continued to put their visitors under considerable pressure, and Valero saw a 20-yard strike deflected wide, before Shovkovsky pushed over a Gomez effort from the centre of the box, although the German did slip as he pulled the trigger.
Dynamo offered little in attack throughout the first half and their chances of progression took a huge blow when Lens was deemed to have dived on the edge of the box five minutes from the break, receiving a second yellow card as a result.
Fiorentina made the extra man pay almost immediately - Gomez guiding in a Joaquin cross with an untidy finish.
Salah caused all sorts of problems for Dynamo at the beginning of the second half, and arguably should have been awarded a penalty when his strike appeared to deflect off the arm of Danilo Silva onto the post.
Dynamo sat back and looked to be waiting for their golden opportunity to pounce.
That moment seemed to have arrived when Rybalka let fly with five minutes left on the clock, but Neto dived to his right to preserve his clean sheet.
Dynamo applied some late pressure to ensure a nervy finish for Fiorentina, but Vargas powered his way into the box to rifle home a second from a tight angle deep into stoppage time to ensure there was no way back for the visitors.