Aase reached the majors when he joined the Red Sox rotation in July 1977. He won his first big league game against the Milwaukee Brewers on July 26 and then threw a shutout against the California Angels five days later. He added another shutout against the Toronto Blue Jays on September 5 and ended his rookie year with a 6-2 record and a 3.12 ERA in 13 starts.
California Angels
Following his first season in the majors, Aase was traded to the California Angels for infielder Jerry Remy. He was primarily a starter in his first two and a half years with the team, notching 11 wins in 1978. In Game Three of the 1979 ALCS on October 5, 1979, Aase became the first member of the Angels to earn a postseason victory. In that contest, he replaced Frank Tanana in the sixth inning with a 2-1 lead over the Baltimore Orioles. He gave up runs in the sixth and seventh innings to blow the lead but still earned the victory when the Angels scored two runs in the bottom of the ninth to win the game and stay alive in the series. Aase was moved to the bullpen in the middle of the 1980 season and was the Angels primary closer in 1981, notching 11 saves. However, in July 1982, he suffered an elbow injury that sidelined him for nearly two years. He came back in June 1984 and made 23 appearances for California, recording 8 saves.
Baltimore Orioles
Following the 1984 season, Aase became a free agent and signed with the Baltimore Orioles. He won 10 games and saved 14 in his first year with the O's before putting up his best numbers of his big league career in 1986. That season, he saved 23 games in the first half and was named to the American League All-Star team. In the only All-Star Game appearance of his career, he came on in the ninth inning with runners on first and third and one out, and earned the save by inducing Chris Brown to hit into a game-ending double play. Later in the season, he began to show signs of overwork. On August 28, he became the first Orioles pitcher to lose two games in the same day, giving up game-winning hits to Dave Kingman in the first game of the doubleheader against the Oakland Athletics and then to Carney Lansford in the nightcap. Nonetheless, Aase set the record for most saves in a season for an Oriole in with 34, surpassing Tim Stoddard's 26 saves in 1980. He held the record until Gregg Olson earned 36 saves in 1990. His 34 saves were also at the time the record for a member of a last place team. Aase's sole win in 1987 came on Opening Day, April 6, pitching an inning and a third of scoreless relief after replacing Mike Boddicker. After a few more relief appearances, he missed the rest of the season with shoulder surgery.
New York Mets
With the season approaching, 34-year-old Aase signed as a free agent with the New York Mets on February 20, 1989. Aase made 49 appearances out of the Mets bullpen in 1989, posting a 1-5 record with a 3.94 ERA over 59 innings.
Los Angeles Dodgers
Exactly one year after coming to terms with the Mets, Aase signed as a free agent with the Los Angeles Dodgers on February 20, 1990. Working out of the Los Angeles bullpen, Aase went 3-1 with a 4.97 ERA over 38 innings in 32 games. His final big league appearance came on the final day of the season, October 3 as the Dodgers hosted the San Diego Padres at Dodger Stadium. With the Dodgers trailing the Padres 4-3, Aase replaced Dennis Cook and let up two unearned runs over one-third of an inning before giving way to Darren Holmes. Aase would become a free agent after the season, but opted to retire.
