Gauff’s main emotion might well have been pride, but her relief at avoiding another early clay-court exit – after losing in the Stuttgart quarter-finals and Madrid last 16 – was also evident.
Struggling with her footwork and misfiring with her forehand, Gauff was way short of her best in the opening two sets.
But, after Jovic missed match point with a tight forehand into the net, the 17th ranked teenager became further distracted by a cut on her finger caused by an earlier fall on the red dirt.
Gauff took full advantage by showing the indomitable spirit which has categorised her ascent to the top of the women’s game.
A flustered Jovic was clearly feeling uncomfortable with her grip and it contributed to a host of errors as Gauff – who has said she is dealing with “tough” off-court issues at the moment – quickly turned the second set in her favour.
Gauff still did not play cleanly in the decider, but knew the importance of simply getting the ball back into play with regularity and preying on Jovic’s problems.
Jovic, who reached the Australian Open quarter-finals earlier this year, continued to hit loosely and her first serve plummeted – as the pair exchanged five breaks of serve – before Gauff steadied herself to win the final three games.
“In my previous round I was not good mentally on the court and this was a complete 180. It shows I can continue to be positive in the most part,” Gauff told Sky Sports.
Later, Poland’s Swiatek, who has teamed up with Rafael Nadal’s former coach Francisco Roig in an attempt to ignite her season, looked far closer to her best as she outplayed Japan’s Osaka.
Swiatek has not won a title since September last year but applied relentless pressure to Osaka, who has rarely looked at home on the clay during her career.
She broke the Osaka serve six times but had another seven break point opportunities, with Osaka winning less than half of the points in her own service games.
Swiatek will play fifth seed Jessica Pegula next after the American beat Anastasia Potapova 7-6 (8-6) 6-2. They are in the opposite side of the draw to Gauff.
In the same section is second seed Elena Rybakina. She was similarly impressive in beating former world number one Karolina Pliskova 6-0 6-2 in 58 minutes to set up a meeting with Ukraine’s Elina Svitolina.
In Gauff’s half, Sorana Cirstea, who knocked out world number one Sabalenka in the last 32, continued her good run by beating Linda Noskova to set up a meeting with former French Open champion Jelena Ostapenko.