- Nicolas Pallois (17')
- Ángel Di María (5', 20' Pen, 78')
Juventus only managed a 1-1 draw against the French side in the home leg as they eyed a long run in the European competition to boost a miserable campaign in which they have been deducted 15 Serie A points for financial irregularities.
"I am happy with the performance, it was not an easy game after the first-leg result, as the crowd here is very passionate," Juve manager Massimiliano Allegri told Sky Sport Italia.
"Just because we were eliminated from the Champions League does not mean it will be easy to win the Europa League. It isn't, but we have the duty to try and go all the way, just as we do in Serie A."
Argentine Di Maria put Juventus ahead after five minutes with a delightful curling strike from the edge of the box into the top corner.
The evening got worse for Nantes after 18 minutes when defender Nicolas Pallois was sent off when he used his arm to stop a another goal from Di Maria. The 35-year-old World Cup winner had no problem converting the resulting penalty.
Juve's Alex Sandro sent in a diving header late in the second half, but Lafont was down quickly to make an impressive one-handed save.
Di Maria completed his treble 12 minutes from time when he sent in a glancing header and the ball just crossed the line before being pushed away.
It was Juve's first hat-trick in a UEFA competition away from home since Filippo Inzaghi in 2000.
"He is a champion and different to the others," Allegri said. "Everything comes easily to him. He raises the overall level of the squad and the others all feel more relaxed in his presence. Di Maria is in the category of real champions."
The draw for the round of 16 will be held on Friday.
- José María Sánchez Martínez