Keuchel captured the American League Gold Glove for pitchers, while Greinke got the National League Gold Glove for pitchers. Both also were among three nominees announced for their league's Cy Young Award.
Arizona Diamondbacks first baseman Paul Goldschmidt also captured a Gold Glove and was announced as a finalist for NL Most Valuable Player.
The reigning AL MVP winner, Los Angeles Angels outfielder Mike Trout, is nominated for the award again. The other nominees are Toronto Blue Jays third baseman Josh Donaldson and Kansas City Royals center fielder Lorenzo Cain.
The NL Manager of the Year candidates are the Joe Maddon, who guided the Cubs to their first playoff berth in seven years during his first season in Chicago; Terry Collins, who led the New York Mets to their first division title since 2006; and Mike Matheny, who guided the St. Louis Cardinals to a major-league-best, 100-win season.
The Texas Rangers' Jeff Banister and the Twins' Paul Molitor both made the short list for AL Manager of the Year in their first season on the job. They are joined by Astros manager A.J. Hinch, who helped Houston end a 10-year playoff drought.
The Royals dominated the Gold Glove honors, capturing three. Catcher Salvador Perez and first baseman Eric Hosmer were each chosen for the third year in a row, and shortstop Alcides Escobar earned his first honor.
Royals left fielder Alex Gordon, a five-time winner, was beaten out by Yoenis Cespedes, who qualified as a Detroit Tiger despite being traded to the New York Mets in late July.
Aside from Molina, the rest of this year's Gold Glove winners all have three trophies or fewer.
The full list of Gold Glove winners:
Zack Greinke, Los Angeles Dodgers (second consecutive Gold Glove)
Yadier Molina, St. Louis Cardinals (eighth consecutive)
Paul Goldschmidt, Arizona Diamondbacks (second overall)
Dee Gordon, Miami Marlins (first)
Brandon Crawford, San Francisco Giants (first)
Nolan Arenado, Colorado Rockies (third consecutive)
Starling Marte, Pittsburgh Pirates (first)
A.J. Pollock, Arizona Diamondbacks (first)
Jason Heyward, St. Louis Cardinals (second consecutive, third overall)
Dallas Keuchel, Houston Astros (second consecutive)
Salvador Perez, Kansas City Royals (third consecutive)
Eric Hosmer, Kansas City Royals (third consecutive)
Jose Altuve, Houston Astros (first)
Alcides Escobar, Kansas City Royals (first)
Manny Machado, Baltimore Orioles (second)
Yoenis Cespedes, Detroit Tigers (first)
Kevin Kiermaier, Tampa Bay Rays (first)
Kole Calhoun, Los Angeles Angels (first)