Bevacqua is notable for his performance during the 1984 World Series when he hit two home runs and had a .412 batting average as the San Diego Padres' designated hitter.

After leading Miami Dade College to the FJCC baseball tournament,[2] he finally signed with the Cincinnati Reds, who selected him in the twelfth round of the secondary phase of the June 1967 draft.

He was traded to the Cleveland Indians for outfielder Buddy Bradford on May 8, 1971, and made his big league debut shortly afterwards.

He appeared in 55 games, playing second, third, shortstop and both corner outfield positions, and earned the nickname "Dirty Kurt" for routinely having the dirtiest uniform on the team.

He was the 1975 Joe Garagiola/Bazooka Bubble gum blowing champion, defeating catcher Johnny Oates in the October finals.

[12] His dream came to fruition on October 22, 1976 when he became the fourth member of the Seattle Mariners, who purchased his contract from the Brewers two weeks before the expansion draft.

[13] He arrived at camp that spring to compete for the shortstop job with Craig Reynolds, whom the club had acquired from the Pirates for relief pitcher Grant Jackson.

[14] Furious over this decision, Bevacqua toyed with the idea of playing ball in Japan, but ultimately decided to sign a minor league deal with the Texas Rangers the day after the season started.

He also disproved Seattle manager Darrell Johnson's assessment that he was a defensive liability as he committed just one error all season while playing five different positions on the field.

After the season, he, Bill Fahey and disgruntled former Rookie of the Year Mike Hargrove were traded to the San Diego Padres for Oscar Gamble and Dave Roberts.

He was batting .268 and on his way to a similar season in 1980 when the last place Padres went into rebuilding mode, and dealt Bevacqua to the Pirates for minor league prospects Luis Salazar and Rick Lancellotti.

Shortly after returning to the Padres, Bevacqua became embroiled in a verbal feud with National League West rival Los Angeles Dodgers manager Tommy Lasorda.

On June 30, Dodgers pitcher Tom Niedenfuer hit Joe Lefebvre with the next pitch after giving up a home run to Broderick Perkins to lead off the ninth.

He's a fucking motherfucking big mouth; I'll tell you that.Bevacqua had in fact been batting .231 with two runs scored, two RBIs and two walks against the Dodgers up to that point in the season.

The final brawl of the evening occurred in the ninth, when Graig Nettles, who homered in his previous at-bat, was hit by Donnie Moore leading off the inning.

[22] With the Padres trailing the heavily favored Detroit Tigers, 3–2, in game one of the series, Bevacqua hit a double to lead off the seventh inning.