An All-American halfback as a junior at the University of California (1948), Jensen scored a touchdown in the team's 20-14 loss to Northwestern in the 1949 Rose Bowl. He was also an All-American pitcher, helping California win the inaugural College World Series in 1947, defeating a Yale team featuring future President George Bush in the final.

In 1950 Jensen left college after his junior year to play in the majors with the Yankees as a backup for Joe DiMaggio. He was sent to the Senators during the 1952 season, and was traded to the Red Sox in 1954.

Making the American League All-Star squad three times and winning a Gold Glove Award at right field, Jensen earned the MVP honors in 1958, when he batted.286, with 35 home runs and a league-leading 116 RBI. He also led the league in RBI in 1955 (116) and 1959 (112); in triples in 1956 (11), and in stolen bases in 1954 (22).

Jensen announced his retirement from baseball in 1960, primarily because of an intense fear of flying. As teams had increasingly turned to air travel in the 1950s, he had unsuccessfully sought to combat this aversion, aided considerably by Red Sox owner Tom Yawkey, who arranged for therapy treatments. Once baseball expanded to the West Coast in 1958, and with further league expansion and constant air travel foreseen, these difficulties became virtually insurmountable. Jensen returned to play in 1961, but frustrated by a sub-par season, he retired again for good. In an 11-season career, Jensen was a .279 hitter with 199 home runs and 929 RBI in 1438 games. He also collected 810 runs, 1463 hits,259 doubles, 45 triples, 143 stolen bases, and a .369 on base percentage. A disciplined hitter, he posted a solid 1.374 walk-to-strikeout ratio (750-to-546).

Following his retirement, Jensen coached baseball at California and the University of Nevada, and also managed in the minor leagues . Jackie Jensen died in Charlottesville, Virginia at age of 55. He was selected to the Boston Red Sox Hall of Fame in 2000.