- Jun 3 Test Cricket debut of Mike Brearley v West Indies (0 & 17)
Belmont Stakes
Jun 5 108th Belmont: Puerto Rican jockey Ángel Cordero Jr., riding Bold Forbes wins his only Belmont classic
- Jun 6 30th NBA Championship: Boston Celtics beat Phoenix Suns, 4 games to 2
- Jun 8 Houston Astros draft Floyd Bannister #1
Golf Major
Jun 13 Canadian Open Golf (Peter Jackson Classic), Cedar Brae CC: Donna Caponi wins in a playoff with Judy Rankin
- Jun 13 French Open Women's Tennis: Sue Barker of England claims her lone major singles title; beats Renáta Tomanová of Czechoslovakia 6-2, 0-6, 6-2
- Jun 13 German sprinter Inge Helten runs female WR 100m (11.04) at Fürth, West Germany
- Jun 14 French Open Men's Tennis: Adriano Panatta of Italy beats American Harold Solomon 6-1, 6-4, 4-6, 7-6 for his lone Grand Slam singles title
- Jun 15 In a blockbuster MLB trade, NY Yankees send May, Martinez, Pagan, MacGregor & Demsey to Baltimore Orioles for Holtzman, Alexander, Grant Jackson, Elrod Henrick & Jim Freeman
- Jun 15 Rain out! Astrodome cancels game heavy rains make it difficult for visiting team and umpires to get through flooded streets to the stadium
- Jun 17 ABA (Nets, Pacers, Nuggets & Spurs) merges into NBA
Sports History
Jun 18 Bowie Kuhn voids Oakland A's sales of players, totaling $35 million - Joe Rudi & Rollie Fingers to Boston Red Sox, and Vida Blue to NY Yankees
- Jun 20 UEFA European Championship Final, Red Star Stadium, Belgrade, Yugoslavia: Czechoslovakia upsets West Germany, 5-3 on penalties following 2-2 draw a.e.t
- Jun 20 US Open Men's Golf, Atlanta AC: Tour rookie Jerry Pate wins his only major title, 2 strokes ahead of runners-up Al Geiberger and Tom Weiskopf
- Jun 22 SD Padre pitcher Randy Jones ties record of 68 innings without a walk
- Jun 25 Texas Ranger Toby Harrah is only shortstop not to handle a fielding chance in doubleheader
Sports History
Jun 26 Japanese professional wrestler Antonio Inoki fights American boxer Muhammad Ali, at the Nippon Budokan in Tokyo, Japan [1]
- Jun 26 Washington Senators player Toby Harrah plays an entire doubleheader at shortstop without a single chance in the field