Carmelo Anthony and the Knicks are headed to the playoffs.
The Knicks hadn't made the playoffs since 2004.
"I think everybody should be excited that Knicks basketball is back, that the standards are higher now and every year this is something we should be looking forward to, which is making the playoffs," Anthony said.
Amare Stoudemire scored 28 points.
"That was the goal we set at the start of the season. The plan was to make the playoffs," Stoudemire said. "It's mission accomplished and now on to the next one."
The Knicks snapped an 11-game losing streak against the Cavaliers to secure their spot. They are seventh in the Eastern Conference, but closed within 1½ games of the 76ers, with a game in Philadelphia this week.
"We knew that this was a game that we needed to get," Billups said. "This team had dominated us the whole season, that team is actually playing a lot better than their record looks like and this is probably the one team that can come in and say that they can beat, because three times they beat us before. So we knew that this was a big game for us."
Anthony scored 25 points and Billups added 23 for New York, which was tied with Minnesota for the NBA's longest playoff absence. The Knicks evened their record at 38-38 as they try to end an even longer drought, a franchise-worst stretch of nine straight losing seasons.
Stoudemire proclaimed the Knicks were back even before officially signing in July, and snapped out of a recent slump in time to ensure the return of playoff basketball to Madison Square Garden.
New York hasn't seen the postseason since it was swept in four games by New Jersey in 2004. The Knicks will likely face either Miami or Boston, hoping Stoudemire, Anthony and Billups can match whichever Big Three they draw.
Billups scored 17 points in the first quarter, and Stoudemire, who had complained recently of being tired after carrying the Knicks before their trade with Denver, helped New York put it away in the fourth.
They were trying to complete what would have been an unprecedented season series sweep. Instead, they fell behind quickly, then nearly erased all of a 22-point deficit before the Knicks pulled away again.
But the Knicks came out with a focus they'd lacked in the previous Cleveland games, storming to a 36-25 lead after one behind 6-of-6 shooting from Billups. New York kept rolling, opening a 61-39 lead on Anthony's jumper with 4:09 remaining in the second quarter.
Davis then hit three 3-pointers before half, bringing the Cavs to 67-57 at the break. Cleveland got as close as two midway through the third, but New York opened it up again with a 12-0 run early in the fourth for a 105-90 lead with 8 minutes remaining.
"We kept battling back. Battling back from 22 down takes a lot out of you," Davis said. "Execution is a huge part of it and I think the turnovers killed us."
Based on reporting by The Associated Press.