During the last play of a red-zone session Tuesday, Derek Carr spotted a defensive deficiency, changed the play at the line of scrimmage and took a quarterback draw into the end zone for an oh-so-easy touchdown.

The score was punctuated with chest bumps and high-decibel cheers from his teammates on offense. And the moment, even if it did come during an offseason practice in May, was worth celebrating.

The reason: It offered evidence that Carr could take a significant step in his third NFL season, which will be his second in offensive coordinator Bill Musgrave’s system.

After practice, Musgrave said Carr doesn’t have to “learn a new language again.” And Carr noted the offensive continuity was the story behind his practice score.

“We wouldn’t have been able to do that last year,” Carr said. “Because we didn’t know the checks. We didn’t know versus certain looks we wanted to do certain things. Just little things like that — we’re already a step ahead. The conversations aren’t, ‘Hey, you know that play we installed today? Where do you want me throw the ball against this coverage?’”

Carr has had a historically strong start to his career. He is one of two quarterbacks to throw for 53 touchdowns in his first two seasons, and he’s the fourth to begin his career with back-to-back seasons with 3,200 passing yards and 20 touchdown passes.

Now there’s a sense the 2015 Pro Bowl alternate could be voted into the all-star game this season, given his comfort level. After all, last season’s 32-touchdown, 3,987-yard performance came after he missed most of the offseason practices with a finger injury while learning Musgrave’s offense.

“Two years in the league; two different systems,” Musgrave said. “Now this year, he can feel he can have a good grasp of it and can put his own spin on things. And he can put his own signature on the system. And (suggest) things he wants to see and tweak a quarter turn here or there. He can initiate that.”

Musgrave welcomes Carr’s input because the 25-year-old has a mind that belies his relative inexperience. It’s a quality that has struck rookie quarterback Connor Cook during his first month with the team. Cook said Carr is like “another coach” and his ability to process information is as impressive as his inability to throw anything less than a perfect spiral. (“I’ve yet to see him throw a wobbly pass,” he said.)

“You just look at how fast he is with the ball,” Cook said. “He knows the type of pressures our defense is going to bring. He can pick it up right now. I’m out there and I’m obviously adjusting and learning and I don’t see it nearly as quickly as he does.

“He’s pointing here. He’s pointing there. He knows the pressure is coming from this side and those guys over there are bluffing.”

Despite Carr’s strong sophomore season, the Raiders’ offense faltered last year after a strong start: Oakland had five of its six 400-yard performances in its first eight games.

For his part, Musgrave said extensive offseason video review helped identify issues and led to offensive tweaks. Carr indicated many of those changes have come after collaboration.

“I had to learn how he wanted things done,” Carr said. “That’s all I’m trying to do. I just want to run his offense the exact way he wants it so he can go home and sleep good. … Now he sees that I’m trying to do that. We’re working together. He comes in the quarterback room all the time asking us questions on what we think. When it’s back and forth like that, he empowers you.”

As it turns out, Tuesday’s practice wasn’t the only example of Carr’s recent strong decision-making. Asked if he attended Game 7 of the Western Conference finals at nearby Oracle Arena on Monday night, he smiled.

“I paid for the seats on my couch,” he said. “I looked at the ticket prices and said, ‘No, thank you.’ My wife would have been upset at me.”

Eric Branch is a San Francisco Chronicle staff writer. Email: ebranch@sfchronicle.com Twitter: Eric_Branch