Rose had 18 points, five rebounds and five assists in 30 minutes, while Wall had 11 points and six assists in 29 minutes.
"When you're on the court, you want to see where a player is," Rose said. "It's just the way I am. I'm always going to attack and make sure a player is on his heels.
"It's challenging, knowing you can guard a guy that fast. It gives me confidence for the next time I'm out there against somebody that mobile. He's a good player."
It was the first professional matchup between Rose and Wall, who both played their college ball under John Calipari. Calipari attended the game and watched his former pupils from a courtside seat behind one of the baskets during the first half, seated next to Indiana coach Tom Crean. Calipari watched the second half with Rose's family.
Kirk Hinrich played his first game in Chicago since being traded from the Bulls to the Wizards before last June's NBA draft. Hinrich, who averaged 13.4 points over seven seasons for the Bulls, scored four points in 28 minutes.
"[It's] a little bit [weird], being in the other locker room," Hinrich said before the game. "I've never seen it before. It was weird the first time I put on this uniform, too, but I've gotten over that."
He received a warm ovation during pregame introductions.
"He don't even look right in that jersey," Rose said.
Kyle Korver added 17 points for Chicago, and Joakim Noah had 12 points and 11 rebounds. Gilbert Arenas led Washington with 16 points.
Rose was the top pick of the 2008 NBA Draft after playing one year under Calipari at Memphis. Wall was the No. 1 overall pick in June following a season under Calipari at Kentucky.
"I told these guys, don't get crazy. It's exhibition," said Calipari, adding that his advice to both players was to be "humble and hungry."
Wall and Rose were relatively quiet in the first half. Wall scored four points and had four assists, while Rose scored six points on 3-of-10 shooting, adding four rebounds and three assists.
The action picked up a bit to start the second half, as Wall and Rose went at each other during several different sequences.
"I thought [Rose] gave us real good flow by getting guys involved and moving the ball," said Bulls coach Tom Thibodeau. "And then in the third quarter, he got real aggressive and took the ball inside."
While the focus was on the point guards, the game was decided on the boards. The Wizards, who have been starting a three-guard lineup, were outrebounded 48-32.
"Our team has to rebound," Wizards coach Flip Saunders said. "It's not our guards getting beat on the glass, it's our bigs."
Korver was 6 of 9 from the field for 14 points in the first half, helping Chicago take a 10-point lead. The Bulls shot 55 percent from the field in the opening half and were 8 of 14 from 3-point range in the game.
The Bulls played their starters through the third quarter while building their 20-point lead. Thibodeau earned his first victory as Bulls coach. Chicago lost its first two preseason games.
Before the game, Saunders said he didn't want Wall to read too much into his first meeting with Rose.
"I think if John has a great game, I don't want him to think he's arrived already," Saunders said. "If he has a bad game, I don't want him to think he's not worth a [darn]. ... I think John will be more excited to play against him than he'll look at it as a measuring stick. John loves to compete, no matter who he plays against.
"[Rose and Wall] play each other four times a year, and [these matchups] are how they're going to be judged."