With the Thunder up by 24 in the fourth quarter, it looked as if Durant and fellow All-Star Russell Westbrook were going to rest for most of the final period.
The Sacramento Kings had another idea, forcing Oklahoma City to make one more push.
Durant scored 31 points, Serge Ibaka added 18 points and 11 rebounds, and the Thunder's starters had to make a late appearance to hold off the Kings for a 113-103 victory Friday night.
It's the franchise's longest winning streak since November 1996, when it won 11 in a row as the Seattle SuperSonics.
"It's good. We're 19-4 and we just want to look at the bigger picture instead of winning streaks," said sixth man Kevin Martin, who had 18 points. "We're a pretty talented team, so we're just taking baby steps and getting better every day."
Sacramento closed to 103-98 thanks to Isaiah Thomas, who scored all 26 of his points in the final 13 1/2 minutes. He had four 3-pointers, a layup and a jumper during a 23-4 comeback attempt by the Kings.
Thunder coach Scott Brooks had already emptied his bench but ended up calling timeout with 4:17 remaining to put his starters back in.
"It was just a little frustration that they came back because I thought we were playing so well," Durant said. "You have tough stretches like that. I was just more frustrated that we gave up the lead."
Durant, Westbrook and Ibaka got the call to come back after Sacramento had cut the deficit to 10. Durant missed his first shot, and Westbrook didn't even catch the rim on his first attempt, with Thomas running right through the defense for a layup in between.
Jimmer Fredette's three free throws with 3:21 left made it 103-98, but that's as close as it got. Fredette couldn't connect on a 3-pointer or a drive to the basket, and Thomas also missed a 3 as Oklahoma City regained its footing.
Durant recovered the ball after getting stripped and dropped in a layup before back-to-back Ibaka baskets extended the lead to 109-98.
"We made it tough, but Scottie has that luxury over there to call the big dogs back into the game," Sacramento coach Keith Smart said. "I thought our guys played and competed."
Durant wrote "Newtown, CT" on both of his shoes as a reference to the deadly school shooting in Connecticut earlier in the day. The three-time NBA scoring champion said it hit him particularly hard because he has a goddaughter who just started kindergarten and cousins in the first and second grades.
A moment of silence was held during the pregame prayer.
"I've got family members that young. Just to see kids that really couldn't do nothing for themselves, couldn't protect themselves, and for their lives to be taken away and for their parents to go through stuff like that, that's the least I could do," Durant said.
"I wish I could do more. But it hit me really hard. It's tough to see, especially kids that couldn't do anything for themselves. Words can't even describe it. I'm kind of at a loss for words right now."
Westbrook had 13 points and 13 assists for Oklahoma City.
After falling behind by 20 late in the first half, the Kings scored the first seven points in the third quarter and a couple minutes later cut the deficit to 65-55 following back-to-back 3-pointers by Aaron Brooks and John Salmons.
The margin was 12 when Smart called a timeout to prevent DeMarcus Cousins from attempting to take the ball coast to coast, then ripped into his players. Whatever he said didn't seem to provide much inspiration. The Thunder restored their 20-point cushion on Martin's two free throws with 9:46 remaining.
"There was a little arguing here and there, but it happens on every team," Thomas said. "Through the toughest times, you've got to know that the guy next to you is going to be all you've got, and we've got to learn that."
The starters weren't quite done yet, and Durant said part of the blame for the comeback should fall on them.
"I'd date that back to the stat of the third. The starters have got to do a better job of coming out with more energy the first five minutes. Then maybe that wouldn't have happened in the fourth," Durant said. "We gave them a little bit of confidence going into that fourth. We just have to be better, and I think we will."
Martin had bookend 3-pointers in a 22-4 surge that put Oklahoma City firmly in control in the second quarter. Ibaka and Durant both had two-handed dunks during the run, and Durant converted a 3-pointer and two free throws.
The Kings went 2-for-9 and committed four turnovers during the stretch before Kendrick Perkins delivered a firm screen to get Martin open for his 3-pointer to make it 56-36 with 2:37 left in the first half.
Sacramento led for just 39 seconds in the game, following a three-point play by Evans late in the first quarter. Martin hit a pair of free throws two possessions later to start a string of seven straight Thunder points, and Oklahoma City didn't trail again.
Reserve guard Marcus Thornton was not with Sacramento for a second straight game for personal reasons. ... The Kings are the only Western Conference team that hasn't beaten the Thunder in Oklahoma City. ... Center Daniel Orton and guard Jeremy Lamb were assigned to Oklahoma City's NBA Development League affiliate in Tulsa before the game.