The sides are set to meet three times in less than a fortnight, with Sunday's Serie A clash to be followed by two encounters in the UEFA Europa League last 16.
Juve enjoyed the majority of possession in the first half at Juventus Stadium, but had to wait until the 42nd minute to break the deadlock through Asamoah.
The victory strengthens Juve's position at the summit of the Italian top flight, with the reigning champions now 14 points clear ahead of the clash between chasing duo Napoli and Roma later on Sunday.
Juve’s incessant pressure finally paid off three minutes before the break as Asamoah pulled off a delightful piece of skill in the penalty area to tee himself up for a right-footed thunderbolt that flew into the back of the net off the right-hand upright via the slightest of deflections.
Vincenzo Montella's men saw a lot more of the ball after the break and came close to an equaliser once again when Mario Gomez headed just wide of the target from a Manuel Pasqual cross from the left.
Fiorentina substitute Ryder Matos took centre stage 10 minutes from time, finding the crossbar with a header from a Vargas cross before going into the referee's book for a dive in the area under the challenge of Chiellini, as Juve lived dangerously in the closing stages.
However, Juve were not to be denied and maintained their perfect Serie A home record this season, which now stands at 14 victories from 14 games.
