The first fight scene of the series was in the first pilot, The Cage, when in illusion Pike fought the Kalar on Rigel VII.
The second fight scene of the series was in the second pilot...
Pike also strangles the Talsian, who I think has crept into the cell to take the phaser.
I wasn't thinking of that as a "fight scene", at least one of significant proportions involving a showcase of choreographed stage combat techniques. But I'll defer to cinematic experts if it's considered one; perhaps I should have said major