A right-handed third baseman, he played parts of two seasons in Major League Baseball for the Baltimore Orioles and Chicago Cubs.

On December 7, Connally was sent to the San Diego Padres as part of a three-team trade involving (among others) Craig Lefferts, Carmelo Martinez, and Scott Sanderson.

Connally spent 1984 with the Las Vegas Stars, the Padres' AAA affiliate, before being traded February 7, 1985, to the Orioles for Vic Rodriguez.

The first came off the Toronto Blue Jays' Doyle Alexander, and the second came at the expense of the Seattle Mariners' Matt Young.

Though he was batting .280 in early June, Connally fell into a 3-for-31 slump, dropping his average to .232, before being sent down to AAA Rochester for the remainder of the campaign.