The sketch show lampooned Giuliani's latest efforts to overturn the result of the 2020 presidential election.
The spoof of the 2000 single, about Davidson's desperate bid to get a Playstation 5 for Christmas, included a surprise appearance from the rapper himself.
"I got tons of strategies. First, we're going to throw out bogus mail-in ballots... these ballots, they could be coming from Mars!" McKinnon's Giuliani explained on the Weekend Update segment.
SNL's cold open saw Jim Carrey's Joe Biden reading a reimagined version of Edgar Allan Poe's poem "The Raven," with McKinnon's Clinton making an appearance in a raven costume.
"If any of you see J.K. Rowling, please tell her... Stick to the books!" McKinnon says in the sketch, where she plays a psychic predicting what 2020 has in store for a group of friends.
The president's personal lawyer was roasted this week after it emerged that Sacha Baron Cohen had duped him for a scene that appears in "Borat Subsequent Moviefilm."
Saturday Night Live joked that the choice between Joe Biden's ABC town hall and NBC's event with the president was a choice between "a Hallmark movie and an alien autopsy."
McKinnon broke the fourth wall during an appearance as Dr. Wayne Wenowdis on the "Weekend Update" segment of the show.
McKinnon paid a touching tribute to the late feminist icon in Saturday Night Live's 46th season premiere.
The Massachusetts senator dropped out of the Democratic presidential race on Thursday.
Earlier this week, the president mocked the teen activist after she was named Time magazine's Person of the Year for 2019.
The show's cold open brought together Kate McKinnon, Cecily Strong and Beck Bennett to riff on the seemingly blind loyalty of congressional Republicans.
Kate McKinnon's Jeff Sessions gets a do-over on his Senate confirmation hearing.
Kate McKinnon channels Forrest Gump to make light of Attorney General Jeff Sessions's very bad week in Washington.
The 'Saturday Night Live' and 'Ghostbusters' joins the cast, along with several other (as yet unnamed) celebrity guest stars.
Standup and actor calls out the 'casual white supremacy' while Beck Bennett's Vladimir Putin assures America he's got its back.
The president-elect wasn't fond of the "Saturday Night Live" treatment of Trump as unprepared and confused.
Alec Baldwin and Kate McKinnon break character in the final sketch before the election.
Host Tom Hanks joins Kate McKinnon and Alec Baldwin as "Saturday Night Live" takes aim at Donald Trump and Hillary Clinton.
'Donald Trump and I disagree on almost everything but I do like how generous he is. Just last Friday he handed me this election," Kate McKinnon's Clinton says.
Alec Baldwin returns as a lecherous, vile Trump who can only "apple-igize" for his comments that condone sexual harassment and assault.
Larry David as Bernie Sanders, Tina Fey as Sarah Palin: Does this influence public opinion?
Jeb Bush, Rand Paul release statements preceding Clinton's, attempting to sway voters.