put on = organize or present a play, exhibition or event
So you could say 'put on a performance' in certain cases where the performance means the actual event ('They put on a great [performance = show]'). I wouldn't say the actor 'put on a great performance'. I might say the actor 'put in a great performance', where:
put in = devote time or effort to (something)
'They put on a play in which the lead actor put in a great performance.'
I think in 'Kobe Bryant putting up a Jordanesque performance', the meaning is similar to 'put in' above. In fact, given the definition:
put up = offer or show (a particular degree of resistance, effort or skill) in a fight or competitive situation, eg 'he put up a brave fight'.
I'd sooner say 'putting in' in this example, as I would in the case of 'he put up a scintillating performance' although the difference in meaning is slight.
Going back to 'put on' - as regards people, I would understand 'put on a performance' as relating to another meaning of 'put on'
put on = assume a particular expression, accent, etc; behave deceptively
'My son might put on a performance if I don't allow him sweets on a Saturday.'
And to combine 'put in' and 'put on':
'Didier Drogba has put in some great performances for Chelsea this season. There's no doubt he's a great player, although sometimes his displays are tainted by charges of gamesmanship, particularly when he's tackled in the penalty area - he has regularly been accused of diving or putting on a performance to try and get a penalty.'