First, Paul walked over to shake hands and exchange congratulations with Paul Pierce following the Celtics’ rugged 97-87 win over Paul’s New Orleans Hornets. In the midst of that conversation, Paul was approached by Celtics guard Rajon Rondo - less than 24 hours away from signing a long-term extension in Boston or staying perhaps only one more season - who said some unkind words to his point guard counterpart.

Paul shot back at Rondo and the two had to be separated. Rondo was ushered to the tunnel by Celtics director of security Phil Lynch, while Paul continued his testy conversation with Celtics assistant coach Tom Thibodeau, and the two were seen yelling at each other while Paul slowly walked to toward the Hornets’ tunnel.

It was the culmination of a passionate clash between two under-25 point guards who each have a point of contention with the other. While many NBA players knuckle-knock, hug, and share laughs after games, hardly fostering any rivalry, it appears Paul and Rondo have an actual disdain for each other.

Paul is a two-time All-Star, one of the faces of the league, a hard worker whose diminutive size and bright smile are deceiving because he is a cut-throat competitor. Rondo, on the other hand, is developing into top-five point guard status, moving into Paul’s neighborhood with a large, noisy moving van that demands respect. He has led his team to an NBA title, Paul hasn’t.

So it’s no surprise that Rondo probably feels slighted when he is considered a second-tier point guard in comparison with Paul and Utah’s Deron Williams.

Paul dropped 22 points on the Celtics last night with 8 assists and 2 steals, making 9 of 13 shots. Rondo tallied 6 points on 3-for-7 shooting with 10 assists and 3 steals. The Celtics won, making Paul wonder why Rondo was so sensitive. Rondo talked with reporters but would not discuss Paul.

The situation began when both were assessed technicals after tangling under the basket with 6:10 left in the second quarter.

“I don’t know, man, they won, that’s all. It was a good game,’’ Paul said. “When you’re winning [you can talk trash].’’

When told he looked upset, Paul, hardly drawn in by the questioning, said, “I just have that expression on my face sometimes. I’m a funny guy like that. I was talking to [Pierce and Ray Allen]; somebody came up to me. I don’t know.’’

In stretches last night, Paul was unstoppable offensively. He’d dart into the lane for the layup and foul. In one sequence, he drew Pierce out to guard him on the perimeter, took one step forward to fake a drive, and then backed up for a 19-footer. He followed by taking out his mouthpiece and uttering some words to Pierce.

As his career has developed, Paul has become a more confident and talkative player. He is no longer an upstart and his success is no longer a surprise. He has put the smaller point guard in vogue again. And he does realize his place in the game. He is the standard for smaller guards such as Rondo.

“They already won the game, what else [does Rondo want to boast about]?’’ Paul said. “I was surprised but, hey, we lost and it was a great game.’’

Paul continued by lauding the Celtics and the players who help make Rondo’s job easier. It was envy mixed with brutal honesty.

“I’m a big advocate for the Boston Celtics and how they defend and how they play hard and play together, it’s something that we want to get to,’’ he said. “Boston has established themselves as a team that’s not going to beat themselves.

“I think Rondo’s a lucky guy to be able to play with a guy like Paul Pierce, Ray Allen, and [Kevin Garnett], Rasheed Wallace. Like I said, man, he’s a great point guard. He has won an NBA championship, something I hope to achieve.’’

Although the Hornets have worked to place solid players around Paul, David West is the lone one remotely comparable with any one of the Big Three.

“They are a great team,’’ Paul continued. “I watch them play on [NBA] League Pass. The way they communicate. KG? I could go on and on about him and the intensity he brings every night.’’

Rondo will know by tomorrow night’s game at Philadelphia whether the Celtics made the same commitment to him as the Hornets did to Paul. New Orleans signed him to a four-year, $68 million extension in the summer of 2008, securing his future.

Rondo is still searching for that security. Perhaps that is why he was a little agitated.

“It’s just a battle,’’ Boston center Kendrick Perkins said. “You’ve got two good point guards, two young point guards, that’s going at it. It’s heated up. They both want to play good against each other. Sometimes you get into a little noise talking, it’s nothing serious I don’t think. It’s nothing personal.

“It started from the first time they got the double-tech. It kept going, but that’s expected. They’re both talented guards that’s young in this league and proving something. When you get a good matchup like that, they’re going to go at it.’’

Paul let it be known he never plans to back down.

“I’m not a big talker,’’ he said. “I’m extremely competitive. I want to win worse than anyone on the court, I guarantee you that.’’

Gary Washburn can be reached at gwashburn@globe.com.