Djere took the second set with ease after jumping out to a 4-0 lead, and the momentum carried over into the third. Fognini found himself in a 4-2 hole, but he proceeded to win the final four games of the set, clinching the victory on his sixth match point.
Fognini was one of three Italians to advance on Wednesday, with No. 4 seed Lorenzo Sonego defeating Sumit Nagal of India 1-6, 6-3, 6-4, and Matteo Berrettini downing Spain's Jaume Munar 6-4, 4-6, 6-3.
However, eighth-seeded Italian Flavio Cobolli stumbled to a 6-1, 7-6 loss against Russia's Pavel Kotov. Kotov will face Fognini, and Berrettini will play Sonego in the quarterfinals.
Estoril Open
Spanish qualifier Pablo Llamas Ruiz cruised to a 6-4, 6-3 sweep of No. 8 seed Dominik Koepfer of Germany in the first round at Estoril, Portugal.
Llamas Ruiz saved six of eight break points and capitalized on five double faults from Koepfer to set up a second-round meeting with lucky loser and countryman David Jorda Sanchis, a 7-6, 6-1 winner over Portuguese qualifier Jaime Faria.
France's Arthur Fils and Gael Monfils, the No. 5 and No. 7 seeds, respectively, both warded off upsets against wildcards hailing from Portugal. Fils beat Joao Sousa, while Monfils knocked off Henrique Rocha.
Other winners Wednesday included Botic Van De Zandschulp of the Netherlands, British qualifier Jan Choinski, Hungary's Marton Fucsovics, Cristian Garin of Chile and Spaniard Pedro Martinez.
US Men's Clay Court Championship
Top-seeded Ben Shelton shook off a slow start to beat Belgium's Zizou Bergs 3-6, 6-4, 6-3 in the second round at Houston.
After dropping the first set, Shelton saved all five break points he faced in the second set, and he never got Bergs a break opportunity in the third.
Shelton was one of three US players to reach the quarter-finals on Wednesday, as seventh-seeded Marcos Giron and Brandon Nakashima also advanced. Giron beat countryman J.J. Wolf 6-4, 6-3, and Nakashima downed Australia's Rinky Hijikata 6-1, 6-4.
In the day's biggest upset, Italy's Luciano Darderi outlasted second-seeded Francisco Cerundolo of Argentina 6-4, 2-6, 7-6 (4).
