During Barber's career, he made the AL All-Star team twice (1963 and 1966) and on April 30, 1967, Barber and Stu Miller combined on a no-hitter that the Orioles would lose to Detroit, 2-1.
Barber pitched 8 2/3 innings and walked 10 and hit two batters. Barber was one out away from the win in the ninth when he threw a wild pitch (his second of the game) with Mickey Stanley at bat that scored pinch runner Dick Tracewski from third base. Miller went on to walk Stanley to put runners on first and third and Miller came in to relieve.
Don Wert was up next and he grounded to shortstop Luis Aparicio who threw to second baseman Mark Belanger for the force, but Belanger dropped the throw and pinch runner Jake Wood scored to put the Tigers ahead 2-1.
The Orioles went down in order (with Frank Robinson leading off!) in the ninth against reliever Fred Gladding. Tigers starter Earl Wilson got the win and gave up only two hits in eight innings and neither hit to led a run. The Orioles lone run came on three walks and a sacrifice fly in the eighth inning.
Two weeks before the combined no-hitter, Barber threw a complete game one-hitter against the California Angels at Anaheim Stadium. Barber was two outs away from a no-hitter when Jim Fregosi doubled in the ninth inning.
In Barber's rookie year of 1960, he threw another one-hitter that was broken up by a hit by Hank Bauer in the sixth inning, who was Barber's manager in 1967.