TiVo stock jumped 6.2 percent to $11.95 per share in after-market trading Tuesday after the television-services provider blew past projections for the fourth quarter.

Earnings of 7 cents per share eclipsed analyst expectations of 4 cents, while revenue of $114 million topped the consensus forecast of $89 million.

San Jose-based TiVo is benefitting from cable customers cutting their cords for video bundles while keeping their high-speed broadband connections.

“Operators are saying we have to figure out a way for our broadband-only customers to relate to video,” CEO Tom Rogers told The Post.

“And they’re thinking our OTA [over-the-air] devices could be an interesting way to do that.”

Rogers, who noted the country already has 15 million OTA-only homes, has reason to be excited about Frontier’s pushing TiVo’s Roamio as the “primary video offering” for broadband-only customers.

The promise of OTA also moved TiVo to buy the trademark and mailing list of Aereo — a defunct TV service that streamed OTA broadcasts for $8 a month — during its bankruptcy auction last week.