CLEVELAND (NBA.com exclusive) --  In ugly games like this, it's about chasing down loose balls as if they're worth a million bucks.

It's about playing with your knees bent, elbows out, and never losing sight of your man on defense. It's not about grabbing every rebound, but getting to the rebounds that count. Mostly, it's about making the biggest stops against the game's brightest stars.

And anyone who witnessed Chicago's 86-85 win in Cleveland on Thursday could see that maybe the Bulls have found their niche. Maybe they will just out-scrap you.

Was the offense pretty? Far from it.

Was the defense perfect? Not really, but it did the job.

Did the Bulls embarrass the Cavaliers on the boards? Well, no. They actually lost that battle (49-43).

Yet somehow, this young team that is still learning found a way in what was the NBA's most difficult arena last season.

"You have to give Chicago credit; they came in here and gutted it out," said Cavs coach Mike Brown. "They were very gritty. They got to a lot of loose balls, especially a couple of them late."

In ugly games like this, that spells victory.

"I was happy with our energy and approach," said Bulls coach Vinny Del Negro. "I thought it was a good team win. Everyone stepped up when we needed them to."

That was particularly true of Bulls big man Joakim Noah. All he did was leap into the air to distract Cleveland's LeBron James near the basket, with the Bulls clinging to a one-point lead and the reigning MVP looking to make a play.

But instead of James saving the day, Noah got his hand on the ball (and a little body on James), causing LeBron to lose it, off his own arm, and out of bounds. Two-tenths of second remained and the Bulls had possession -- of the ball and of their first win in Ohio in two seasons.

It earned Noah the right to stand in the middle of the locker room afterward, smiling and saying to no one in particular, "It's a good day to be in Cleveland."

He then summed it up this way: "It's a big win for us. When our offense starts clicking, we're gonna be even tougher."

Noah spoke the truth, as the Bulls' offense far from clicked. They shot less than 41 percent (36-of-88) from the floor. Their leading scorer, Luol Deng, finished with just 15 points.

And their most accurate shooter in the starting lineup? Try rookie Taj Gibson (5-of-12, 11 points), who was playing in just his fifth NBA game.

But in the Bulls' defense, at least they were better than the Cavs. James was his usual superhero-like self, finishing with 25 points, seven boards and six assists. Other than that, the Cavs looked out of sync and at times, overmatched.

And while the Bulls often made the rim cringe with fear, the Cavs were even worse, making 40.7 percent of their field-goal attempts and shooting just 60 percent on free throws.

"In a one-point game, we shot 60 percent from the free-throw line," Brown said. "We had our chances and we didn't pull it out. That's why every night, no matter who you play, it's going to be a dog fight."

Deng, who is making an early case for the All-Star game, spent most of the night harassing James and grabbed seven rebounds.

Point guard Derrick Rose, who played a magnificent second half, finished with 14 points and 11 assists. He also hit the game's final basket. John Salmons scored 14 and Gibson added 11.

"We play hard, that's all I can say," Rose said. "We trust each other now. If you don't have any trust, there's no point in being out there."

Shaquille O'Neal added 14 points and 10 rebounds for the Cavs, and Anderson Varejao tallied 12 and 13, respectively.

The Cavs have already lost their second home game, something they didn't do last season until the final day, in dropping to 3-3.

"I think we're still learning," James said. "I think defensively with a new team you can always be on the same page...On the offensive end, it takes a little longer."

The Cavs are showing that now, having been hot and cold in each of their six games. Still, O'Neal said it's not yet time to panic.

"We have a lot of resolve," he said. "In the three games we've lost, we pretty much beat ourselves by what we're not doing. Once we master that, we'll be fine."