At 17 years, 70 days old, Gauff is the youngest player to sweep the singles and doubles titles at an event since Maria Sharapova won both titles at 2004 Birmingham, at 17 years, 55 days old.
The 19-year-old, who will head to Roland Garros in a fortnight as defending French Open champion, beat Karolina Pliskova 6-0, 6-0 in the final in Rome at the weekend to climb six places to ninth, leapfrogging her Czech opponent who slips to tenth.
Italian Open: Perfect 10 for flawless Rafael Nadal, Iga Swiatek rewinds to Paris — talking points from Rome
Rafael Nadal and Iga Swiatek, the defending French Open champions, won the titles in Rome to mark an anchor for Roland Garros that gets underway on 30 May.
Swiatek has now won three titles, following on from Roland Garros with Adelaide in January, and now Rome, and will move into the top 10 for the first time on Monday.
On Sunday, Djokovic again felt the full, raw power of Nadal on clay as the Spaniard clinched a 10th Italian Open title with a 7-5, 1-6, 6-3 win in the final.
Second seed Nadal won through 7-5, 1-6, 6-3 in 2hr 49min against the defending champion in the 57th career showdown between the pair.
The 19-year-old reigning French Open champion took just 45 minutes to dispatch the 2019 Rome winner two weeks before she opens her title defence in Roland Garros.
Italian Open: Novak Djokovic beats Lorenzo Sonego to set up title clash with Rafael Nadal; Iga Swiatek enters final
Djokovic and Nadal, who will be facing each other for the 57th time, last played in the 2020 French Open final which the Spaniard won in straight sets.
Italian Open: Rafael Nadal, Karolina Pliskova through to final, Novak Djokovic beats Stefanos Tsitsipas
Playing his 500th clay-court match, Nadal staved off break points in the fourth game of the first set and did not look back to win through in 1hr 32min.
Italian Open 2021: Ashleigh Barty retires injured in quarter-final, Karolina Pliskova beats Jelena Ostapenko
Top seed Barty, the 2019 French Open champion, was leading 6-4, 2-1 when she pulled up to receive treatment during her match against American Coco Gauff.
Italian Open: Ashleigh Barty retires from quarter-final against Coco Gauff; Rafael Nadal gets revenge over Alexander Zverev
Second-seed Nadal had lost to Zverev in the Madrid last-eight last week.
Nine-time champion Nadal had to save two match points against Canada's Denis Shapovalov in a 3-6, 6-4, 7-6 (7/3) battle over nearly 3hr 30min.
The top-seeded Barty won through 6-3, 6-3 to set up a clash with US teenager Coco Gauff who earlier ousted Madrid winner Aryna Sabalenka.
Italian Open: Novak Djokovic sails into quarter-finals with straight-set win over Alejandro Davidovich Fokina
The five-time Rome champion won through 6-2, 6-1 in 1 hour and 10 minutes against the 48th-ranked Spaniard with the venue filled to 25 percent of capacity.
Italian Open: Rafael Nadal overcomes Jannik Sinner to reach third round; Daniil Medvedev suffers defeat
Rafael Nadal won through 7-5, 6-4 in two-hours 10-minutes to bring his record to 16-1 in his opening matches in the Foro Italico.
The 39-year-old eighth seed fell 7-6 (8/6), 7-5 in under just two hours to the 44th-ranked Argentine, a surprise semi-finalist at last year's Roland Garros.
Italian Open: Top seed Ashleigh Barty enters third round with staright sets win over Yaroslava Shvedova
Barty overcame an early break of serve to see off Shvedova, a three-time Grand Slam quarter-finalist making her way back after giving birth to twins.
The four-time Grand Slam winner, seeded second in the Italian capital, had received a first-round bye, but was unable to find her way back into the match after losing the first-set tie-break to her 31st-ranked opponent.
Thiem won 3-6, 7-6 (7/5), 6-0 in two hours and 33 minutes against 44th-ranked Fucsovics in the clay-court tournament which acts as a warm-up for the French Open in which the Austrian has twice finished runner-up.
Italian Open: Novak Djokovic overcomes 'strange' three-hour rain delay to reach third round after beating Taylor Fritz
Djokovic, 33, playing his second tournament since winning his ninth Australian Open in February, will play Cameron Norrie or Alejandro Davidovich for a place in the quarter-finals.