"His wife actually sent me a letter congratulating me," Jaster says of Alexander's widow. "I have it in my closet."
The southpaw carried his shutout string into the seventh inning of his next start against the Dodgers in April 1967, finally giving up a one-out sacrifice fly to Jeff Torborg in an 8-4 victory.
A velocity-sapping shoulder injury, however, prevented Jaster from delivering on the promise of 1966, when he finished fourth in voting for National League rookie of the year.
Though Jaster was 9-5 against the Dodgers, his 35-33 career record included only two other shutouts, the last a two-hitter against Tom Seaver and the New York Mets in May 1968. He was only 4-16 after developing a "frozen shoulder" later in '68.
"I really wasn't effective after that," he said. "I could pitch without pain, but it wasn't the same coming out of my hand. The life wasn't there, the velocity wasn't there."
After giving up a grand slam to Jim Northrup of the Detroit Tigers in Game 6 of the 1968 World Series, Jaster was claimed by the Montreal Expos in the expansion draft. In 1969, he was the Expos' starter in their first game at Montreal.
He made his last major league appearance in 1972, finished up in Triple A and returned to school to get his degree, eventually earning a master's in physical education at the University of New Mexico while also pursuing a coaching career.
A father of three, Jaster is a longtime minor league pitching coach now working in the Orioles organization.
Occasionally, he says, someone will ask him about his phenomenal success against the '66 Dodgers.
"The more time goes on," he says, "the more you think, 'Man, I guess that was something different.' You get more and more proud of it."
"The longer it went on, the more they were pressured to stop it, which worked in my favor. They were pressing, and I kind of rolled along, thinking there was nothing to it."