Juve's have won all 14 home games although it was a close call as Fiorentina substitute Ryder Matos headed against the crossbar with 10 minutes to go.
Both teams were without their playmakers as Juve's Andrea Pirlo and Fiorentina's Borja Valero were both suspended.
Juventus attacked relentlessly in the first half and nearly went ahead when Fiorentina goalkeeper Neto made a reflex save to block Asamoah's deflected shot.
Asamoah was wide from the corner, Paul Podga volleyed over from a good position and Juan Manuel Vargas cleared off the line as Juventus continued to pour forward.
They finally went ahead in the 42nd minute when Asamoah burst into the Fiorentina area and, despite being surrounded by four defenders, made space with a clever dragback and fired a right-foot shot into the top corner.
"The coach keeps telling me to cut in and try shooting from that angle," the Ghanaian told Sky Sport Italia. "It's the first with my right foot and I am very happy."
Juventus have 72 points from 27 games, 14 clear of second-placed AS Roma who are away to third-placed Napoli later
Image: Kwadwo Asamoah celebrates after scoring
Photograph: Valerio Pennicino/Getty Images
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