Seven-time champions Lyon took an early lead through Brazilian forward Catarina Macario and were huge favourites as they dominated early proceedings.
But the French powerhouses were reduced to 10 players just after the hour when Ellie Carpenter was sent off for a foul.
Launched just five years ago, the Italians had never been at this stage of the Champions League but had a lively crowd in the Juventus stadium willing them on.
A storming finish ensued with a leveller when fast-thinking Cristiana Girelli pounced on a loose ball on 71 minutes, before a brilliant shot from the just introduced substitute Bonfantini on 81 minutes won the night.
Londoners Arsenal take on Germans Wolfsburg later Wednesday.
On Tuesday Barcelona came from behind to beat Real Madrid 3-1 away with a double from Alexia Putellas.
Paris Saint-Germain striker Marie-Antoinette Katoto also scored twice as they won 2-1 away to Bayern Munich.
Quarter-finals
First leg
Juventus (ITA) 2 (Girelli 71, Bonfantini 83) Lyon (FRA) 1 (Macario 8)
Arsenal (ENG) 1 (Wubben-Moy 89) Wolfsburg (GER) 1 (Wassmuth 19)
Played Tuesday
Bayern Munich (GER) 1 (Buehl 84) Paris Saint-Germain (FRA) 2 (Katoto 20, 71)
Real Madrid (ESP) 1 (Carmona 8) Barcelona (ESP) 3 (Putellas 53-pen, 90+4, Pina 81)
