WINSTON-SALEM, N.C. - Top seed Gilles Simon of France was upset by Britain's Aljaz Bedene, while two other high seeds survived upset bids on Tuesday during second-round play at the Winston-Salem Open.

Bedene, ranked 58th in the world, battled through tiebreakers in all three sets and match point in the third against the 11th-ranked Simon to win 6-7 (5), 7-6 (5), 7-6 (6).

Meanwhile, 15th-ranked Kevin Anderson of South Africa, the No. 2 seed, beat Kazahkstan's Mikhail Kukushkin 4-6, 6-2, 6-3. Third-seeded Jo-Wilfried Tsonga of France, ranked 19th, downed Uzbekistan's Denis Istomin 5-7, 6-4, 6-1 at the Wake Forest Tennis Center in the final tuneup for next week's U.S. Open.

It was Bedene's fourth career win over a Top 20 opponent since turning pro in 2008, and his third this season. Before Tuesday, Bedene's previous career best came against then-No. 14 Feliciano Lopez of Spain in the round of 16 in Chennai, India, in January.

"I haven't beaten (someone) in the top 10 yet, so this is my best win," the 26-year-old Bedene said. "It was tough. Gilles is known as one of the toughest guys on the tour. Coming back after losing the first set, and having served for it, is never easy. But I'm playing well. I can't wait for my next match."

His victory came in just the 12th ATP World Tour match this season to have tiebreakers in all three sets — three of those coming Tuesday at the Winston-Salem Open. Earlier in the day, Russia's Teymuraz Gabashvili beat Australia's Thanasi Kokkinakis 7-6 (5), 6-7 (5), 7-6 (3); while Italy's Simone Bolleli needed just over 2 1/2 hours to defeat seventh-seeded Sam Querrey of the U.S., 7-6 (7), 6-7 (4), 7-6 (9).

"(Simon) was returning well, and I was returning well," Bedene said. "We did not have so much advantage with our serve. Sometimes there were games (40)-zero, sometimes there were long ones.

"It was a close match — three tiebreaks. I don't think I've ever played on the ATP Tour three tiebreaks."

Simon had an opportunity to close out the third-set tiebreaker and win the match, going up 6-5 after getting a mini-break on Bedene's serve. But Bedene got his own mini-break to even the score at 6-6, then won the next two points.

"I had my chances to win this match," Simon said. "But Aljaz always played some great shots in the right moments to save some of them.

"I really tried to put everything I had on the court today, but my game just wasn't good enough and Aljaz deserved to win."

Simon and Querrey were among eight seeded players to fall Tuesday. Tunisia's Malek Jaziri upset fourth-seeded Viktor Troicki of Serbia 6-4, 4-6, 6-4; Taiwan's Yen-Hsun Lu downed fifth-seeded Guillermo Garcia-Lopez of Spain 6-3, 6-3; South Korea's Hyeon Chung beat No. 9 seed Benoit Paire of France 6-1, 6-4; Spain's Pablo Carreno Busta defeated 10th-seeded Joao Sousa of Portugal 6-4, 6-4; Argentina's Diego Schwartzman downed 12th-seeded Pablo Andujar of Spain 4-6, 7-5, 7-5; and France's Pierre-Hugues Herbert defeated 14th-seeded Marcos Baghdatis of Cyprus 6-3, 2-6, 7-5.

Also winning Tuesday was American Steve Johnson, 2014 finalist Jerzy Janowicz of Poland, 11th-seeded Jiri Vesely of the Czech Republic and sixth-seeded Thomaz Bellucci of Brazil.

Johnson, seeded 13th and the only American player remaining, beat Australia's Sam Groth 6-4, 6-7 (4), 6-1.

Janowicz needed just less than 71 minutes to defeat defending champion Lukas Rosol of the Czech Republic 6-3, 6-2. Last year, Rosol rallied past Janowicz 3-6, 7-6 (3), 7-5.

Vesely beat Slovakia's Martin Klizan 6-3, 6-4; and Bellucci downed American qualifier Frances Tiafoe 6-3, 2-6, 7-6 (2).