Stubbs made his Major League debut as the starting first baseman for the Dodgers on April 28, 1984, against the San Diego Padres.

His first hit was a triple off Kent Tekulve of the Pittsburgh Pirates on May 5 and his first home run was off Charles Hudson of the Philadelphia Phillies on May 14.

Playing for the Dodgers in 1987, Stubbs had 885 total chances and made only 5 errors for a .994 fielding percentage, leading the National League.

The trade was made after Stubbs had spent the entire prior season as a backup, having lost his starting role to Eddie Murray.

He signed as a free agent with the Montreal Expos on February 22, 1993, but was released at the end of spring training on March 29.

He was promoted to the AA Chattanooga Lookouts in 2011-12 and became the hitting coach for the Albuquerque Isotopes, the Triple-A affiliate of the Dodgers in 2013.

A year later, he was promoted to hitting coach of the Hillsboro Hops, the Arizona Diamondbacks Class A Advanced affiliate.