In other results on Tuesday (Wednesday AEDT), record eight-time winners Lyon eased past tournament debutants Galatasaray 3-0, Chelsea held on to beat Real Madrid 3-2, and Dutch side Twente won 2-0 at Celtic.
The most impressive performance belonged to Roma, considering they finished bottom in last season's group stage.
"It's a huge victory, a result that we wanted at all costs," Roma coach Alessandro Spugna said.
"I think it is our best (result) in Europe. We delivered an intelligent performance, understanding the game and managing the difficult moments well."
In the other Group A match, all of Lyon's goals were headers, with France striker Kadidiatou Diani getting two of them.
After Lyon lost the final to Barcelona last season, Lyon's coach Sonia Bompastor left to replace Emma Hayes at Chelsea. Bompastor's new side was in charge for long spells at Stamford Bridge, before sloppy defending gave Madrid a late lifeline.
In Rome, the home side took the lead early at Tre Fontane stadium through captain Manuela Giugliano's 14th-minute penalty following a foul by right-back Lynn Wilms.
Wolfsburg striker Alexandra Popp made her 99th competition appearance and is one away from becoming only the second player to reach 100, after Lyon's Wendie Renard.
But it was defender Marina Hegering who was Wolfsburg's most dangerous threat, twice going close with headers as the 2023 runners-up chased an equaliser.
Goalkeeper Camelia Ceasar made several saves to keep out the German side.
Lyon won the trophy five consecutive times during their heyday and were runners-up last season to Barcelona.
Diani headed in a 34th-minute cross from Mali winger Tabitha Chawinga, who assisted again moments before the break with a looping left-wing cross to give Canada's Vanessa Gilles an easy header from near the goal line.
Galatasaray goalkeeper Gamze Yaman denied Lyon, before Diani nodded in Amel Majri's left-wing cross in the 77th minute.
Bompastor was replaced at Lyon by Joe Montemurro, and French hopes firmly rest with his side after Paris Saint-Germain - semi-finalists last season - were eliminated by Juventus in qualifying.
Chelsea's Sjoeke Nusken (second left) scored the opening goal against Real Madrid. (AP PHOTO)
Hayes left Chelsea to lead the US women and immediately made her mark with gold at the Paris Olympics.
Not seeing her patrolling the touchline must have felt unfamiliar for home fans after her 12 years in charge at Stamford Bridge, which included a semi-final loss to Barcelona last season.
But they were cheering in the second minute when Sjoeke Nusken forced the ball in after challenging for Johanna Rytting Kaneryd's cross with Madrid defender Sheila Garcia.
Midfielder Guro Reiten's crisp penalty made it 2-0, but Madrid pulled one back shortly before the break when forward Alba Redondo's low shot went through the legs of goalkeeper Zecira Musovic.
A looping header from Colombia striker Mayra Ramirez made it 3-1 early in the second half.
Chelsea looked in control, but some muddled defending led to a scramble and Colombian Linda Caicedo pounced for the Spanish side in the 84th minute. The home side managed to hold on for a 3-2 result.
In Group B's other game, midfielder Kayleigh van Dooren struck in each half as Dutch side Twente won 2-0 at Celtic.
Barcelona's quest for a third straight title begins on Wednesday (Thursday AEDT) with a trip to Manchester City, while Swedish club Hammarby face St Polten of Austria in the other Group D game.
Arsenal face a tough trip to German champions Bayern Munich in Group C, with Norwegians Valerenga hosting Juventus in the other match.
14°C