Jiménez was regarded as an outstanding minor league hitter. In his first full professional season in 1958, he led the Northern League with a .340 batting average while playing for the Eau Claire Braves. After hitting .325 for the Pacific Coast League Vancouver Mounties in 1961, he was acquired by the Athletics in a multi-player trade.

He made his major league debut on April 11, 1962 against the Minnesota Twins at Kansas City Municipal Stadium. He was the starting left fielder, batting fifth against Minnesota ace Camilo Pascual. The Athletics were victims of a four-hit shutout, but Jiménez went 3-for-4 against the All-Star right-hander. He was well on his way to a memorable rookie season in which he hit .301 (eighth in the American League) with 11 home runs and 69 runs batted in.

In July 1962 owner Charles O. Finley met with Jiménez and told him to "stop concentrating on hitting for average and concentrate on hitting more home runs." Jimenez went into a slump and lost about 30 points off his average during the last two months of the season. Finley at first denied any interference but later admitted to reporters that he had indeed met with Jiménez after the manager and coaches had "unsuccessfully tried to do the same thing."

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