Captain Kirk and Commander Spock had their most famous duel in the episode "Amok Time" by Theordore Sturgeon This dramatic battle, driven by Spock's fiercely libidinal urges, is one of the best in classic Star Trek.
It's a great story on par with those seen in professional wrestling. It is thus appropriate that Mega Championship Wrestling conducted a match at, I think, ColossalCon 2024. Both competitors work the crowds, building tension to a passionate climax. It ends in a close embrace as Spock uses a special Vulcan technique to finish off his best friend.
You can see the full match below.
-via Holodeck Four