Swift was spotted with a number of A-list friends at the Allegiant Stadium cheering on her boyfriend, Chiefs tight end Travis Kelce, as his team beat the San Francisco 49ers in overtime.
Shortly after the match, Mr Biden shared a "Dark Brandon" meme, which showed laser beams blasting out of the president's eyes.
"Just like we drew it up," the caption of Mr Biden's post read.
Mr Biden's post appears to be in response to a conspiracy theory floated by Republicans that Swift's popularity would be leveraged by the Democrats to swing the 2024 presidential election.
The Dark Brandon meme is used by critics of the president to mock his perceived weakness, presenting him ironically as a dark and threatening force. Brandon is a reference to an incident in late 2021 when a Nascar reporter seemingly misheard a crowd chanting “f*** Joe Biden” as “Let’s go Brandon”.
This isn’t the first time Mr Biden has sought to subvert the meme – it was deployed as the image for the 404 error page on his official campaign website that launched last summer.
Swift endorsed the Biden-Harris ticket in 2020 and has previously suggested she could have done more to criticise Donald Trump in 2016.
Last year nonprofit Vote.org recorded more than 35,000 registrations after Swift posted a message on Instagram encouraging her 280 million followers to register to vote.
Former president Donald Trump earlier on Sunday rued that it would be "disloyal" for Ms Swift to endorse Mr Biden as the Democratic president "did not do anything" for her.
"I signed and was responsible for the Music Modernization Act for Taylor Swift and all other Musical Artists,” Mr Trump wrote on Truth Social, referring to a 2018 bill.
Mr Trump continued: “Joe Biden didn’t do anything for Taylor, and never will. There’s no way she could endorse Crooked Joe Biden, the worst and most corrupt President in the History of our Country, and be disloyal to the man who made her so much money.
“Besides that, I like her boyfriend, Travis, even though he may be a Liberal, and probably can’t stand me!” he added.
During the game, Swift was joined in the private box by A-listers including Hollywood actor Blake Lively, rapper Ice Spice and pop artist Lana Del Rey, along with the Chiefs’ family and friends.
Swift could be seen chugging beer and slamming her empty cup down on the table, in between cheering enthusiastically for Kelce – or else biting her nails whenever the 49ers pulled ahead.
In a separate post, Mr Biden congratulated the Chiefs, saying: “With their third Super Bowl win in just five seasons, the Kansas City Chiefs aren’t just champions today – they’re a dynasty.”
With their third Super Bowl win in just five seasons, the Kansas City Chiefs aren’t just champions today – they’re a dynasty.
Congratulations, Chiefs Kingdom.
Ready to welcome this team back to the White House. pic.twitter.com/8GZDRiopRX
— President Biden (@POTUS) February 12, 2024
“Ready to welcome this team back to the White House,” he added.