Raducanu was competing in the last 16 for the first time in her career, but was no match for the Madrid Open finalist who took one hour and 21 minutes to book her place in the quarter-finals at the Foro Italico.
With her new coach Mark Petchey watching on, Britain's number two struggled against Gauff’s powerful forehand and lost the opening set in just 40 minutes.
Raducanu came from one set down to beat Veronika Kudermetova in the previous round but all hopes of another famous comeback were extinguished in the blazing sunshine in Rome.
Gauff broke serve in the fifth game to lead 3-2 and won two tie-breaks on her way to reaching the last eight for the second year in a row.
"Emma’s a tough opponent so I’m really happy with how I played," Gauff told Sky Sports.
"I’m hoping to redeem myself here (after reaching the final in Madrid). My forehand was a big weapon… it set me up for a lot of good points."