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.
Fiorentina threatened to battle their way back into the tie after the break, with Modibo Diakite having a goal disallowed, but Juve held out to avenge their sole league defeat of the season, which came in the reverse fixture back in October.
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.
Antonio Conte welcomed Giorgio Chiellini and Arturo Vidal back from injury and suspension respectively, and it was the hosts who applied the early pressure amid an intense atmosphere in Turin, with Carlos Tevez seeing an effort deflected wide by Gonzalo Rodriguez in the opening five minutes.
Stephan Lichtsteiner should have put Juve in front 10 minutes later when he received the ball from a Vidal cut-back, but skewed his attempt wide of the left-hand post.
Fiorentina were struggling to get out of their own half, with home goalkeeper Gianluigi Buffon reduced to the role of spectator, and Tevez failed to bring the ball under control when clean through on goal in the 24th minute, knocking the ball out for a goal-kick as Juve continued to press.
The visitors had Neto to thank for keeping the game goalless two minutes later when he punched behind from a deflected Asamoah strike, before Paul Pogba lofted a volley over the crossbar.
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.
Diakite looked to have pulled Fiorentina level early in the second period, but his strike was ruled out for offside.
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.
Juan Manuel Vargas was next to get a sight of goal in the 68th minute, but sent the ball well over the crossbar of a grateful Buffon.
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.
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