Bruce Sutter: 1979
Bruce Sutter was a truly remarkable relief pitcher and arguably the most dominant closer of the 70s and 80s. In 1979, he became one of only nine pitchers to ever win a Cy Young when he led the league in saves with 37 and struck out 110 batters in 101.1 innings pitched with a 2.22 ERA.
Again, by modern standards, Sutter probably shouldn't have won the Cy Young award. Starters Joe Niekro and J.R. Richard both had career seasons where they each surpassed 250 innings pitched. Richard was particularly fantastic, with a 2.71 ERA and 313 strikeouts. But this was way before the Reliever of the Year award was even invented, and Sutter was able to sway enough voters with his dominant closing abilities.
To this day, Sutter has the second most saves in Cubs history (133) even though he only spent five seasons with the club.