Tenace was selected in baseball's first entry draft in 1965, being taken in the 20th round by the then Kansas City Athletics. Tenace made his major league debut in Oakland during the 1969 season, playing his first two years as an anonymous third catcher before serving as Dave Duncan's backup in 1971.

Tenace entered the 1972 season backing up Duncan, but became the team's regular catcher in the postseason. He put himself in the spotlight during Game 1 of the 1972 World Series, when he became the first player to homer in his first two World Series at-bats. He went 8 for 23 in the Series, with 4 home runs, to earn the World Series MVP Award.

Tenace's heroics helped him earn a full-time job in Oakland's lineup. He served as the team's starting first baseman for 2 seasons, while still serving as the backup catcher. He had his roles reversed in 1975, starting at catcher while backing up first base. As a regular starter for the A's, Tenace had a low batting average but a fair amount of power, hitting 20 home runs in 4 consecutive years in Oakland, finishing among the top 10 home run hitters in the American League each year. He further made up for his lack of a high batting average by sporting a tremendous batting eye. He drew over 100 walks in a season three times for Oakland, and led the AL in walks in 1974, making up for a career-low .211 average that year. His best year with Oakland might have been in 1975, when he hit a career-high 29 home runs, drew 106 walks, finished 18th in the MVP voting and started his only All-Star Game.

Tenace was one of several Athletics who became free agents after the 1976 season and participated in a newly created re-entry draft, in which teams acquired the rights to negotiate with veteran free agents. Tenace and teammate Rollie Fingers were the first players from that draft to sign, with both joining the San Diego Padres in December of that year. In 4 years as a starter with the Padres, his power numbers dropped in part due to the cavernous dimensions of San Diego Stadium, only reaching 20 home runs once; but his batting eye remained, recording 3 more seasons of 100 walks, with a career best of 125 in 1977. He recorded an on base percentage of over .390 in each of his years in San Diego, and finished 3rd in the National League in that department in 3 consecutive years.

After the 1980 season, Tenace, Fingers, and two others joined the St. Louis Cardinals in a trade for Terry Kennedy and 6 minor leaguers (Fingers was then traded to the Milwaukee Brewers four days later). In his two years in St. Louis, Tenace primarily played against left-handed batters, platooning with Darrell Porter. He was part of the Cardinals team that won the World Series in 1982.

He played his final season as a pinch-hitter for the Pittsburgh Pirates in 1983, and retired after being released the following year in spring training.

He retired with a .241 average and 201 home runs, but had a fine on-base percentage of .388, among the best for players during his era. Remarkably, less than half of his career trips to first base came via base hits, reaching 1,075 times through walks (984) and being hit by pitches (91) as opposed to only 1,060 hits.

Appropriately, Tenace became a hitting coach after retiring as a player. He was a hitting coach for the Toronto Blue Jays in 1991 when manager Cito Gaston was sidelined with a herniated disc. Tenace served as the team's interim manager for 33 games while Gaston recovered, going 19-14 and keeping Toronto competitive en route to an eventual division title. Tenace stayed with Toronto during their consecutive World Series championships in the following two years, giving him 6 rings in 6 World Series appearances as a player and a coach.