Tatum's professional career began when he signed with the Angels in 1966 after he was selected in the second round of the secondary phase of the 1966 Major League Baseball Draft. In his fourth minor league season, in, he was converted from a starting pitcher to a relief role, and he was recalled by the Angels in May. He quickly established himself as the team's top short reliever—the term "closer" was not then in use. By the end of July, he had amassed seven saves and three wins in relief, with an earned run average of 0.95 in 21 games. He finished the year with a win-loss record of 7–2, 22 saves, and an earned run average of 1.36 in 45 games pitched. He placed fourth in American League Rookie of the Year balloting. Tatum began with another skein of excellent relief pitching. During the season's first two months, he appeared in 20 games, won two of three decisions, netted eight saves, and posted a 1.00 ERA in 27 innings pitched. But in the eighth inning of his 20th appearance on May 31, while he was in the process of notching a four-inning save in a 6–1 victory over the Baltimore Orioles, Tatum threw a pitch that hit the Orioles' Paul Blair in the face. The pitch broke Blair's cheekbone and nose and he missed three weeks of action; his vision, however, was not affected. He remained the Orioles' regular center fielder through, and retired from the Majors during the campaign.
But the incident may have been a turning point that ruined Tatum's career. Affected by Blair's traumatic injury, he became reluctant to pitch inside. By August 1, his earned run average rose by two full points to 3.00 and it would climb as high as 3.30 on August 30 before he was able to string together enough effective appearances to lower it to 2.94 at season's end. For the year, he went 7–4 with 17 saves in 62 games. Wrote Peter Gammons in 2013: "After retired, he admitted he pitched with the fear 'that I might kill someone. I could never pitch on the inside half of the plate again.'" Ten days after the 1970 season ended, the Angels traded Tatum to the Red Sox in a six-player swap that brought slugger Tony Conigliaro to Anaheim. But Tatum was ineffective in Boston. In his first game, on April 8, 1971, he blew a 2–1 ninth-inning lead for Sonny Siebert and lost to the Cleveland Indians on a walk-off single to Gomer Hodge. Tatum recovered to pitch well over his next 16 games, but on May 23, he was injured by a line drive to the face during batting practice. Coincidentally, he fractured his cheekbone, and the injury occurred in Baltimore, with Blair still an Oriole stalwart. Tatum would miss afull month of action, and his pitching suffered. He ended the season having worked in only 36 games, with a 2–4 record, 4.09 earned run average and only nine saves. Troubled by a nerve problem in his back and leg, he would appear in only 22 games in, and spend most of in the minor leagues before Boston included him in an off-season trade to the St. Louis Cardinals. After spending the spring training of with the Redbirds, he was traded again in April, to the White Sox, where he got into ten games. He retired at the close of that season. All told, Tatum compiled a 16–12 record in the big leagues with 52 saves and a career ERA of 2.93. He allowed 230 hits and 117 bases on balls in 282 innings pitched, with 156 strikeouts.
