The second seed entertained the crowd under the roof on Court One with big hitting to earn a 6-2 6-1 victory in 66 minutes.
A second convincing win this week marks progress for the American at SW19 after a surprise exit in the first round last year."I realised what I do, yes I'm passionate about, but it's not that serious and sometimes the world can make you feel like there's so much pressure, so much expectation.Todoni, 19, came into Wednesday's match on the back of a dominant win - and her first victory in a Grand Slam - over fellow qualifier Olga Danilovic, of Serbia.
But she faced a tougher opponent in US Open winner Gauff, who is among the favourites to go the distance at Wimbledon.It was an uphill task from there for Todoni, who struggled to absorb Gauff's powerful ball striking and won just three points on her opponent's serve.