Pulisic was instrumental in the United States' opening win, assisting Folarin Balogun's first goal and playing a part in the move that led to Paraguay's own goal, before being substituted at half-time after taking a knock to his calf. Manager Mauricio Pochettino has since played down concerns over the injury.
Giroud, who played alongside Pulisic at Chelsea until the 2020-21 season and later again at AC Milan after Pulisic's move to Italy, spoke to BBC Sport about what made his former team-mate such an effective partner in attack.
"Christian reminded me of Eden Hazard for the way he took on opponents and the ease with which he dribbled past people."
The French striker, now playing for Lille after departing Major League Soccer, explained how Pulisic's qualities complemented his own style as a target man during their time together at Stamford Bridge.
"I played as an advanced reference point and I needed speed and movement around me, someone like him who played between the lines, received the ball, looked for me and took advantage of my flick-ons."
Giroud said he was not surprised by Pulisic's performance against Paraguay, pointing to qualities he believes can lift the United States as the tournament progresses.
"I wasn't surprised by how well he played against Paraguay, because I think he has what it takes to help the United States team make a step up in quality in the coming weeks."
The 39-year-old also reflected on the nickname Pulisic carried during their time together at Milan, a reflection of his standing within the American game even when not wearing the captain's armband for his country.
"At Milan we called him by his nickname, 'Captain America', because even when he wasn't wearing the United States captain's armband, he was their main player, the one with the highest profile."
Giroud went on to stress how important Pulisic's contribution would be if the United States are to progress beyond the group stage, while tempering expectations about the tournament as a whole.
"I've always thought the United States are lucky to have him, because he has talent and intelligence. Nobody expects the United States to win this World Cup, but if they want to reach the knockout stage, he will be essential."
With Pulisic expected to be available for the United States' next fixture barring any setback with his calf, Giroud's comments add to the growing sense that the co-hosts' attacking quality, built around players who have proven themselves at the highest level in Europe, gives them a platform to make a genuine impression in the tournament.