All three players were fined along with Yankees manager Joe Girardi, third-base coach Bobby Meacham and hitting coach Kevin Long.
The suspensions, unless appealed, will start at the beginning of the regular season.
Bob Watson, baseball's vice president for discipline, cited Duncan for "violent and reckless actions, which incited the bench-clearing incident," and penalized Cabrera for "violent and aggressive actions during the incident."
Gomes was suspended for "violent actions, which escalated" the situation.
Benches cleared during the second inning of Wednesday's game, four days after Girardi complained about Tampa Bay's aggressive play after a collision at the plate that injured catcher Francisco Cervelli.
"I really haven't had much time to really analyze it," Duncan said after playing against Cincinnati in Sarasota, Fla. "Initially, I feel it is pretty unfair. After the incident with Cervelli, I was asked a question about I feel about it and how I was going to approach the next game. For some reason people assumed I made retaliatory remarks, which I never did. When asked how I was going to play the game, I told everyone that asked me, I was going to play the game hard. I was going to match their intensity, or even exceed it."
Duncan said he isn't sure if he will appeal the suspension.
Duncan slid into Rays second baseman Akinori Iwamura with spikes raised after hitting a hard grounder off third baseman Evan Longoria's glove and trying to advance to second base on the play.
Duncan, thrown out by at least 10 feet, was immediately tossed. Gomes was ejected after racing in from right field and barreling into Duncan as other players poured onto the field. No punches appeared to have been thrown as order was restored.
