Their lead lasted only three minutes as Mario Mandzukic equalised with an instinctive volleyed finish after reacting to a loose ball in the area.
The Croatian striker then put Juve in front with his fourth league goal in four games, heading home Patrice Evra's cross from the left four minutes before the interval.
It was three for Juve shortly after half time as Paul Pogba got in on the act with a low finish after being found with a ball over the top.
That made it comfortable for Juve, but there was a tense finish for the champions after Leonardo Bonucci's calamitous own goal in the 92nd minute.
Carpi immediately won the ball back and had a golden chance to salvage an unlikely draw, but Lorenzo Lollo failed to make a decent connection from eight yards.
Three points sees Juve climb up to second, but they will drop back to fourth if Fiorentina and Napoli win later today.