The Juve winger struck just before half time to cement the Old Lady's position at the top of Serie A.
Furthermore, it gives Antonio Conte's men confidence for their next two meetings with the Viola in the last 16 of the Europa League.
Fiorentina are the only team to have beaten Juve in Serie A all season and without the suspended Andrea Pirlo, the Bianconeri could well have feared for their flawless record at home this season.
There was no need for that concern in the first half, though, as Juve stamped their authority on the game, leaving Fiorentina chasing shadows, and the ball.
Conte's men failed to do much with their possession, however, and a long ball which just touched the toe end of a full-stretch Carlos Tevez was indicative of how they were not quite getting to that final ball.
Asamoah had two good chances with a volley deflected behind and another shot just missing the far post, and it was a case of third time lucky for the Juve winger, who scored just before half-time.
Asamoah skipped into the penalty area with a trick taking him past three Fiorentina defenders before his shot deflected into the far corner, off the inside of the post.
Fiorentina responded well in the second half, but the first big chance fell at the other end with Tevez getting to the goal line and pulling the ball back towards Fernando Llorente, who would have had an easy tap-in had the ball not been so weak that keeper Neto could intercept.
Two minutes later, Mario Gomez headed over from eight yards out, wasting his one and only chance of the game.
He was replaced by Ryder Matos with 20 minutes to go, and his first touch could and probably should have resulted in an equaliser.
He sent a free header against the crossbar with Gomez perhaps wishing he had been given such an opportunity.
Juve defended their lead well with Gianluigi Buffon racing off his line and out of his box to beat Juan Cuadrado to a long ball, taking the ball down on his chest before sending it to the other end of the field as Juve preserved their perfect home record, and took another step towards a third straight Serie A title.