Yost found Moylan, the 37-year-old Australian with the side-winding delivery.
After appearing in 21 games in May, June and July, Moylan became Yost's bullpen workhorse, appearing in 29 games over the last eight weeks and posting a 2.25 ERA.
"We've been taking the whip to him," Yost said, shaking his head.
And going into Thursday's game against the Twins, Moylan had appeared in five straight games. The franchise record is six by Ted Abernathy in 1970.
Moylan's 50 appearances are his most since 2010. He has a 3.43 ERA.
"He's doing great," Yost said.