Rodon, 23, matched the mark set by Joe Cowley of the White Sox on May 28, 1986, at Texas. The major league record to start a game is eight strikeouts set by Houston's Jim Deshaies in 1986 and matched by Jacob deGrom of the New York Mets in 2014.
Four of Rodon's strikeouts came on sliders, two on fastballs and one on a changeup. He got John Ryan Murphy looking on a 97 mph fastball to lead off the third. Logan Schafer ended the streak with a double to right.
Rodon struck out 11 in his previous outing, including the final three hitters he faced, in a win Sunday at Cleveland.
Rodon was the third overall draft pick by the White Sox in 2014.