O'Donoghue was primarily a starting pitcher during the first half of his major league career, and almost exclusively a reliever during the second half. From 1963–1967, he started in 93 of his 139 games, and from 1968–1971 relieved in 115 of his 118 games. He struggled greatly during his first four minor league seasons, from rookie ball to Double-A. He had a combined record of 26–39 with an earned run average of 5.54. In 499 innings pitched he had given up 307 earned runs, struck out 360, and walked 358. In 1963, at the age of 24, it all began to come together. Pitching in the Eastern League and Pacific Coast League, he had a combined record of 14–11 with an ERA of 3.10, leading to his call-up to the pitching-starved Athletics. O'Donoghue made his major league debut on September 29, 1963, the last day of the regular season. He was the starting pitcher in a home game against the Cleveland Indians at Municipal Stadium. He gave up just two runs in six innings, but was the losing pitcher as Jim "Mudcat" Grant and the Tribe prevailed, 2–1. His first major league career win came on May 12, 1964 at Dodger Stadium. He started and pitched the first seven innings against the Los Angeles Angels, giving up two unearned runs, and the A's won by a score of 6–2. John Wyatt saved the game for him with two scoreless innings. O'Donoghue's finest major league effort was against the Detroit Tigers on August 19, 1967. He pitched a one-hit complete game shutout at Tiger Stadium that day, striking out 11 and walking only 2. The Tigers had such players as Dick McAuliffe, Al Kaline, Willie Horton, Bill Freehan, Eddie Mathews, and Norm Cash in the lineup, but O'Donoghue was almost untouchable. Freehan got the only Tiger hit, a 2nd-inning single, as the Indians won 5–0. Even though O'Donoghue was named to the American LeagueAll-Star team in 1965, it probably does not qualify as his best season. He was 9–18 with a 3.95 ERA; the 18 losses tied him for the league lead with Boston Red Sox pitchers Bill Monbouquette and Dave Morehead. In 1967, he compiled an 8–9 record with a 3.24 ERA and had his lowest career WHIP. Then, in 1969, he relieved in 55 games for the Seattle Pilots and compiled a 2–2 record with 6 saves and a 2.96 ERA in 70 innings. O'Donoghue was traded along with Gordon Lund by the Indians to the Baltimore Orioles for Eddie Fisher and minor leaguers Johnny Scruggs and Bob Scott on November 28, 1967.
"We talk a lot about not drawing fans. At the same time most of the players are still telling the fans they'll be fined $50 if they sign any autographs. If some of the guys spent as much time signing autographs as they do shooing kids we'd have a lot more friends around here. Chief kid-shooer is O'Donoghue. He enjoys the work. One of these days he's going to make another Frank Crosetti." — Jim Bouton in Ball Four
