On July 26, 1984, Roger Clemens pitched his first big league shutout. The AP summarized:
Roger Clemens pitched a four-hitter and struck out 11 in his first major-league shutout to give the Red Sox a three-game sweep of the Chicago White Sox, 7-0, in Boston.
Clemens (4-4) didn’t allow a runner beyond second base and struck out Ron Kittle four times. Clemens had lost three straight since June 22.
“This is definitely the best game I’ve ever pitched, since I first picked up a baseball,” he said. “I can’t describe how happy I am. I’ve waited a long time for this.”
A month later, on August 21, he dominated the Royals at Fenway. The game summary:
Roger Clemens struck out 15 batters, the most strikeouts by a Boston pitcher in 23 years, as the Red Sox routed the Kansas City Royals, 11-1, tonight.
Jim Rice hit his 299th career homer and drove in four runs while Tony Armas added a three-run homer.
Clemens, a 22-year-old rookie right-hander, recorded the most strikeouts for a Red Sox pitcher since Bill Monboquette struck out 17 Washington Senator batters in 1961.
Clemens (8-4) allowed seven hits and did not walk a batter. He struck out the side in the fourth inning en route to his fifth straight victory.
You can also read about Clemens’ 20-strikeout game in 1986.