IRVING, Texas—Brad Johnson didn’t mind the boos. He gladly traded them for a victory.

In his second start subbing for injured Tony Romo, Johnson repeatedly threw passes that probably wouldn’t get first downs but also likely wouldn’t be intercepted. His safety-first approach annoyed the home fans—until the Dallas Cowboys walked away 13-9 winners over the Tampa Bay Buccaneers on Sunday.

Johnson passed for a measly 122 yards and the Cowboys gained only 172, their fewest ever in a victory. His aim was off on several potential scores, but he came through on a 2-...

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