Third-seeded Gilles Muller of Luxembourg and sixth-seeded Adrian Mannarino of France reached the quarterfinals. Muller topped Victor Estrella Burgos of the Dominican Republic 7-6 (7) 6-4, and Mannarino rallied to edge Australia's Sam Groth 7-6 (6) 6-3.
The 31-year-old Baghdatis kissed the court when the match ended after giving a long embrace at the net to longtime friend Sela. The Cypriot is seeking his fifth career ATP title.
"We know each other from a very young age," Baghdatis said. "A lot of emotions."
The tournament is held on the grounds of the International Tennis Hall of Fame. Marat Safin and Justine Henin head the 2016 class that's set to be enshrined during a center-court ceremony Saturday. Play was delayed for nearly three hours by rain after Mannarino won the first set.
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Second-seeded Ivo Karlovic of Croatia, a finalist in Newport the last two year, had his quarterfinal match against Switzerland's Marco Chiudinelli postponed until Friday. Mannarino said that playing inside the stadium helped him relax.
Once play resumed, Mannarino continued his strong play. "I was just trying to focus on my game (during the delay) and what I have to do," he said. "It worked pretty well. When I got back on court I was pretty consistent."
On Tuesday, Mannarino said of a side court: "The court is just ridiculously bad. We're playing (next to) the other court. You've got the camera, the microphone on the court. You can't really move. This is really not respectful for the players to come, that kind of court."
Mannarino entered the week ranked 55th on the ATP tour.