After spending 1957 in the minor leagues, he played 43 games for the Dodgers (now in Los Angeles) in 1958, then became the regular center fielder for much of the 1959 season, helping the team defeat the Chicago White Sox in the 1959 World Series.

September 1962 was the start of 266 consecutive errorless games for Demeter in the outfield, a Major League record that would stand for almost 30 years, until Darren Lewis broke the mark in 1994.

In 1966, he lost playing time to Mickey Stanley and Jim Northrup, appearing in only 32 games before getting traded to the Boston Red Sox on June 14.

Demeter attended Capitol Hill High School, where, as a center fielder, he helped the baseball team win the state championship in both his junior (1952) and senior (1953) year.

[24] The next day against the Cardinals, Demeter recorded his first major league hit and home run, driving a 2–1 pitch from Don Liddle into the left field stands to contribute to a 17–2 victory.

[27] National League (NL) president Warren Giles gave him very high praise, saying that he "should make the grade as a regular with the Dodgers next season.

[29] Brooklyn President Walter O'Malley announced during the Japan tour his plans to move Snider over to left field to make room for Demeter in center.

[43] At the start of the 1958 season, The Sporting News listed Demeter as the "kid with greatest potential" and the "best bet for batting title" in the Dodgers' organization.

[44] After serving a six-month term with the Army in San Antonio, Texas, Demeter was discharged on April 17, 1958 and left to immediately join the major league Dodgers in Los Angeles.

In 12 at bats, he hit .250, scoring two runs as the Dodgers defeated the Chicago White Sox in six games for their first World Series championship in Los Angeles.

[72] He started the majority of the team's games in center field until July 3, where he fractured his wrist on the road against the Pittsburgh Pirates after colliding with Los Angeles shortstop Maury Wills.

Mauch remarked, "There aren't many better center fielders around than he is, and you can put it in the book right now that he'll hit more than 20 home runs any year he plays a full season in our park.

Over the course of the year, he had to sit out for a week in May with a pulled groin muscle, several more days in June after a jammed middle finger on his right hand, and four times with a left knee injury, with the fourth occurrence shutting him down for the short remainder of the season.

[89] On August 15 against the New York Mets, he attained a unique feat, hitting two home runs that day off two separate players named Bob Miller.

Don Nottebart of Houston held the Phillies hitless, but in the fifth inning, Demeter hit a ground ball past J. C. Hartman, resulting in what was recorded as a two-base error.

[112] Demeter suffered another minor injury on July 28 when Drysdale of the Dodgers hit him on his right forearm, resulting in several more missed games.

[118] On December 5, 1963, the Phillies traded Demeter and reliever Jack Hamilton to the Detroit Tigers for catcher Gus Triandos and eventual Hall of Famer Jim Bunning.

[126] On April 29, he hit a decisive home run in the top of the 10th inning against John Wyatt of the Kansas City Athletics, leading the Tigers to a 5–4 win.

[131] On July 31, Demeter set an MLB record with 206 consecutive errorless games in the outfield, passing former Phillies teammate Tony González's mark of 205.

[137] On February 5 in Tulsa, Oklahoma, Demeter was given the Art Griggs Award, presented annually to Oklahomans with the most outstanding performance at the major league level.

[150][151] He suffered another injury against the Angels on August 27, damaging his left wrist while trying to make a diving catch on a line drive hit by Jimmy Piersall.

"[164] Later, against the Baltimore Orioles on May 21, Demeter started a six-run rally in the fourth inning with a three-run home run off pitcher John Miller to tie the game 4–4.

[159] On June 14, 1966, Demeter and Julio Navarro were traded by the Tigers to the Boston Red Sox for outfielder Joe Christopher and pitcher Earl Wilson.

Rookie Reggie Smith looked to be the new starting center fielder, with Jose Tartabull to be his backup, leaving Demeter as the odd man out.

[178] Against Kansas City on June 19, with two men out in the bottom of the ninth and one man on base, he pinch-hit for pitcher Sonny Siebert, hitting a game-tying home run in an eventual 2–1 victory for Cleveland.

He had already reported for spring training in Tucson, Arizona and successfully passed a complete physical examination, but he decided to end his career anyway due to the potential for future heart trouble.

[2] Writing for the Society for American Baseball Research in 2007, Jonathan Arnold said Demeter was "a very highly regarded player during his career, [though] he is largely a forgotten man now.

[1] As a junior in high school in 1950, Demeter met his future wife, Betty Jo Madole, at the Exchange Avenue Baptist Church during a social event.

[2] Two of Don's grandchildren, Cole and Caden Cleveland, were All-State ballplayers at Christian Heritage Academy in Del City, Oklahoma before playing National Collegiate Athletic Association (NCAA) Division 1 college baseball at Morehead State University in Kentucky.

[5] After winning the World Series with the Dodgers in 1959, Demeter returned home to Oklahoma City to spend the winter as a youth director at a Baptist church.