RIYADH, Saudi Arabia — While Saudi Arabia counted down the hours until midnight for the ban on women driving to be lifted, Hessah Alajaji ran out of patience.

She put on some lipstick, jumped in the driver’s seat of her parents’ Lexus, and at 9:10 p.m. drove out for dinner.

“I’m a bit naughty,” she said, laughing over the melody of Saudi pop tunes as she cruised the wide highway linking north and south Riyadh, the Saudi capital. “I’m just so excited.

Ms. Alajaji, 33, was one of an elite group of female drivers who succeeded in getting their driver’s licenses in time to mark this historic day, one that erases her homeland’s dubious distinction as the last nation in the world in which women could not drive.