"I think the frustrating part is we had an opportunity to win and, regardless of what anybody says, it's going to be hard for us to win a game when I play that bad," said Paul, who missed 12 of 14 shots and ended up with nine points and nine assists.
"It's tough because you work so hard but there's going to be nights like that."
Los Angeles had been tied with Memphis for the West's best record at the start of the day but dropped behind Oklahoma City and San Antonio with the loss. The Clippers were trying to win at least seven games in a row for only the sixth time in franchise history, and the first time since 1991.
"We fought the whole game and Chris got a great look. We're going to live and die on that shot," Jordan said. "We fought but we definitely made some mistakes tonight. They made more plays than we did down the stretch."
Matt Barnes scored 19 points while replacing starting forward Caron Butler in the Clippers' lineup. Butler missed the game with a strained right shoulder sustained Monday night in a win at San Antonio.
Kevin Martin scored 20 points and Serge Ibaka chipped in 15 points and 12 rebounds for Oklahoma City before fouling out in overtime. Hasheem Thabeet also matched his career high with 10 points off the bench.
The Clippers won three out of four against Oklahoma City in a sometimes testy series last season that included Griffin's memorable throwdown over Perkins in a Clippers win and Perkins' retaliation with a hard foul to Griffin's face as Oklahoma City won the rematch.
Barnes had a couple scuffles with Ibaka and Perkins but nothing quite as noteworthy.
The Clippers ended up with a 54-38 edge scoring in the paint and a 28-10 advantage in second-chance points. Oklahoma City made up for it by making 34 of 39 free throws, while L.A. was 24 for 33.