The Crew (8-15-6, 30 points) raced to a 3-0 lead on goals by Zardes in the 22nd and 33rd minutes and the dagger by Diaz in the first minute of stoppage time before 30,611 fans.
Expansion Cincinnati (5-19-3, 18 points), which has six losses and a tie in its past seven matches, got an 89th-minute goal by former Crew forward Kekuta Manneh.
Columbus is 3-1-4 in the past eight games.
The match was the opposite of the first time the Ohio rivals met in MLS play on Aug. 10 in Columbus when the Crew spotted FCC a two-goal lead before rallying for a 2-2 final in the "Hell Is Real" derby.
Zardes, who did not travel Wednesday when the Crew lost 1-0 at New York City FC, scored off an early ball by Diaz for the 1-0 lead.
FCC, which has allowed a league-high 64 goals, is 0-15-1 when conceding the first goal.
The second of three straight Crew goals down the right flank resulted in Zardes' 11th goal of the season and seventh in the past 10 games.
Diaz scored off the second assist of the game for Pedro Santos. Diaz made a long run then scored from a bad angle to the near post for the 20-year-old Costa Rican's first MLS goal in eight games since being signed July 2.
Cincinnati has allowed three or more goals four times in the first half to lead MLS.
Crew goalkeeper Eloy Room lost a chance at his first MLS shutout in his seventh game when Manneh scored from close range for his fourth goal.
Room had five saves. Tyton made three saves.