Here's Woody Allen on The Jack Paar Show. I don't think this is from The Tonight Show. I think it's from the show Paar hosted after he left the late night slot. He had a prime-time show on NBC for a while which was basically the same program but shorter, earlier and once a week.
Merv Griffin used to tell people that Allen owed his career to him. The way Merv told it, Paar had Woody on once or twice, didn't like him and told the producers not to book him again. Then one night, Merv guest-hosted for Paar and the producers told him he could have any guests he wanted as long as they weren't folks that Paar considered "his" regulars. One of the people Griffin asked for was Woody Allen…who came on and did so well that his spot drew raves from a couple of TV critics. Those reviews, in turn, prompted Paar to give the comedian another chance and he caught on big after that. Griffin was annoyed that thereafter, Paar took a great deal of credit for Woody Allen's success and no mention was made of the role Merv had played.
I don't know if that's true or not. I think Woody does credit Paar…but he also appeared often with Merv and seemed to have a loyalty to him, as well. Anyway, here's this appearance with Paar, which is said to be from 1964…