Saturday Night Live, 1978
Jane Curtin and Bill Murray, Saturday Night Live, 1978
The Saturday Night Live in the question first aired on March 25th, 1978. Here's a transcript of a sketch called Weekend Update from season 3, episode 15:
Jane Curtin: ... And now, with this week's movie news, here is the Party Animal himself -- Bill Murray.
Bill Murray: Thank you, Jane. [ he holds up his Oscar board ] Well, the Oscars are coming up, April 3rd, and here are my predictions, everybody. ...
Let me throw it back to a future Oscar winner, and a girl who's at least a half a party animal herself -- Jane Curtin. Get out of here, Jane, you're terrific!
Jane Curtin: Thank you, Bill!
SNL "party animal": 1977, 1978, 1980
And whilst we have the SNL transcripts handy, here's a whole load more, mostly from Bill Murray in Weekend Update.
Bill Murray, The New Guy, season 2: episode 16, March 19th, 1977:
[Fade in on recently-hired cast member Bill Murray who sits at a desk, addressing the camera.]
Bill Murray: Hello, I'm Bill Murray. You can call me "Billy" but, around here, everybody just calls me "The New Guy." ...
Last Friday, I went to a party with Danny. There was a pretty girl there I wanted to impress and, uh, I'm a party animal. I was very funny. Danny said nothing. He was saving it. She said to me, "You're so funny! I wish I had a tape recorder." Well, I wish she had, too, you know? Saturday night, after the show, when she went home with Dan, I could've played the tape back for her.
Bill Murray, Baba Wawa At Large sketch, season 2: episode 21, May 14th, 1977:
Richard Burton [played by Bill Murray]: They HATE me! They DESPISE me! And just because I'm a PARTY ANIMAL!! I like to PARTY! PARTY! PARTY! And they DON'T!!
Bill Murray, Weekend Update, season 3: episode 1, September 24th, 1977:
Bill Murray: Thank you, Jane. Hello, everybody. And I mean that. Now, get out of here! I love you! I hope everyone had a primo summer. Yours Truly, the Party Animal, went totally insane for three months!
Bill Murray, Weekend Update, season 3: episode 19, May 13th, 1978:
Bill Murray: Thank you, Jane. Well, just like all the other critics in this country, I gave my Oscar predictions the week before the Academy Awards. But unlike all those other critics, tonight I'm here to 'fess up on just how badly I did. Uh, pretty damn badly, I'm afraid. Other than Diane Keaton's nod for Best Actress, the party animal here completely struck out.
Bill Murray, Weekend Update, season 5: episode 14, March 15th, 1980:
Bill Murray: ... I gotta say: Ayatollah, if you wanna go, if you wanna get loony - I know you, you're a nut - if you wanna go, you know, go festive. Let loose the party animal within you, okay? Go completely nuts! [ puts lampshade on Ayatollah dummy ] Now, get out of here, you crazy Komeiniac! Get outta here! Jane?
SNL "party animals": 1977
Finally, the earliest I found is in the plural and isn't by spoken Bill Murray, but he's also in the sketch.
John Belushi, The Wild Bees Motorcycle Club sketch, Mardi Gras Special, February 20th, 1977:
Jake the Snake [played by John Belushi]: [ blows smoke at Rhonda's face ] You know what your gonna do?! You're comin' back to California with me! Come back to your block house! Listen! I'm an ANIMAL!! I call party animals, animals from parties! anything will do! We'll shave your head and chain you to the roof and wipe our feet on 'ya! And then we'll make 'ya pick up after us! Whattaya say?! you wanna come?! [ thrusts her to the ground ]