Aereo claims that it is just making it easier for customers to exercise their right to access free over-the-air television.
But the broadcasters argue that Aereo must pay for permission to re-transmit their signals, just like cable and satellite providers already do.
"This Court should... eliminate the massive loophole the Second Circuit has created in Congress’ carefully crafted copyright regime," the TV companies wrote.
They warned that if the lower court decision stands, it would encourage cable providers and other Internet companies to use similar techniques to avoid paying copyright holders.
“We will respond, as appropriate, in due course," Virginia Lam, spokeswoman for Aereo, said.
The key legal question is whether Aereo's service qualifies as a "public performance" under copyright law. In July, the Second Circuit sided with Aereo, but the Ninth Circuit granted the broadcasters' request to shut down a similar video service called FilmOn X in August.
Although the Supreme Court declines to consider most of the petitions it receives, it is more likely to intervene in a case if there is a split between the circuits on an important legal question.
The broadcasters are represented by lawyers including former Solicitor General Paul Clement, who argued against the president's healthcare law before the Supreme Court last year.