For the second straight preseason game, 49ers rookie C.J. Beathard will serve as the second-string quarterback when the 49ers visit Minnesota on Sunday night.

Beathard was the No. 3 quarterback in the preseason opener behind Matt Barkley, 26, but the third-round pick could secure the backup spot with another strong performance. He’s completed 14 of 23 passes for 211 yards with three touchdowns (130.6 passer rating) in the preseason.

Shanahan explained his rationale for keeping Beathard at No. 2.

“I wanted to get C.J. (in the game) earlier,” Shanahan said. “I’ve seen Barkley play in the NFL before. I’d like to see C.J. do it a little bit more.”

Shanahan was clearly referencing Beathard’s inexperience, but the fact is Barkley’s career has been underwhelming. Of the 63 quarterbacks who have thrown 250 passes since 2013, Barkley’s passer rating (63.7) ranks last and his completion percentage (59.8) is 41st.

Meanwhile, Beathard received more good news Friday. His grandfather, former NFL executive Bobby Beathard, 80, was announced as a finalist for the Pro Football Hall of fame by the contributor’s committee. Beathard will be inducted if he receives 80 percent of the vote from the selection committee in February.

“Everyone I’ve known that has known my grandpa has good things to say about him — he’s as good a human being as there is,” Beathard said. “ … He’s the most down-to-earth, humble person you’ll ever be around. You wouldn’t know who he is by speaking to him.”

Safety sitting: Shanahan said safety Jimmie Ward won’t play Sunday after he was removed the physically unable to perform list Wednesday.

Ward, the starting free safety, had been sidelined since sustaining a hamstring injury on July 27 when the 49ers reported for training camp. If the 49ers rest their starters in the preseason finale Thursday, which is customary, Ward will debut in the season opener against the Panthers on Sept. 10.

Ward, who missed the final two games last year with a broken collarbone, hasn’t played in a game since Dec. 18.

Shan’s plan: Shanahan expects the starters to play at least the first two quarters Sunday.

“My goal is to at least keep them in the first half,” Shanahan said. “That’s what I’d hope for. Then I’ll get a feel at halftime what we want to do in the third quarter.”

The 49ers will be particularly eager to see their offense get untracked. The starters have had three punts and three turnovers in six preseason drives.

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

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