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Tampa Bay Lighting winger J.T. Brown didn't get all of his aggression out on the ice Monday night -- smashing a fan's iPhone moments after he was sent to the penalty box after an all-out brawl.

Brown went straight Conor McGregor on Nashville Predator defenseman Ryan Ellis after a blindside hit in the 3rd period.

As Brown was sent off the ice, Preds fan Brendan Johansen began to heckle him ... and that's when Brown reached up and smashed the cell phone.

We spoke with Johansen who says he's not mad and isn't taking any legal action -- but says he hopes the Lightning will spring to get him a new phone ... because his screen got shattered in the mayhem.