A Tesla Inc. rally Monday took the stock above a symbolic threshold of $420 a share, the price at which Chief Executive Elon Musk last year said he wanted to take the electric-vehicle maker private.

The new height also represents a U-turn in investor confidence in the Silicon Valley auto maker, whose shares this year closed as low as $178.97. A surprising third-quarter profit, the unveiling of a new pickup truck and progress toward building Model 3 compact cars in China have fueled the stock’s rise.

After...