Palmer graduated from Norte Del Rio High School and attended American River College, both in Sacramento. He was selected by the Philadelphia Phillies in the first round (sixth overall) of the 1966 Major League Baseball Draft (Secondary Phase). Palmer was called up to the Phillies after posting a 36–17 won–lost record in 3.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1⁄2 minor league seasons, with 534 strikeouts in 516 innings pitched.
He made his major league debut on June 21, 1969, with a starting assignment against the Pittsburgh Pirates at Connie Mack Stadium. He held Pittsburgh scoreless through the game's first six innings, but unraveled in the seventh and eighth innings, permitting five earned runs; he was tagged with the Phils' 8–2 defeat.
Palmer threw a three-hit, complete game and shutout in his third MLB appearance, against the Montreal Expos at Jarry Park Stadium on June 29, but overall he struggled to a 2–8 record in 1969, with a 5.20 earned run average, in 29 games during his rookie campaign. He would throw only one more complete game in his major-league career, that coming in his final season. In Palmer's MLB tenure as a member of the Phillies (1969–1971), St. Louis Cardinals (1972), Cleveland Indians (1972) and San Diego Padres (1974), he posted a career record of 5–18; his earned run average for in his 106 career MLB appearances (with 25 starts) was 5.29.

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