Buffalo has not won a playoff game since beating the Miami Dolphins in the 1995 AFC Wild Card round.
The prize for Jacksonville should they beat Buffalo is a trip to Pittsburgh again in the Divisional Round, and it's the last thing the Steelers want to see.
But three wins in four to end the season and a bit of help from Cincinnati ended the longest play-off drought in all of United States sport.
Marrone used an option in his contract to opt out after the Bills changed ownership after the 2014 season.
After Tyrod Taylor was knocked out of the game with a head injury in the final two minutes, Nathan Peterman entered at quarterback for the Bills. "But the type of game like this, you've got to lay it all on the line". There were questions about whether he'd play after he had to be carted off the field in Week 17, but he's doing just fine, thank you. The drive culminated in Blake Bortles' 1-yard touchdown pass to Ben Koyack with 49 seconds remaining in the quarter.
The Jaguars were finally able to move the ball on the final drive of the half.
You can watch the National Football League playoffs on Now TV with prices starting at £6.99 for a Sports Pass. McCoy rushed for 1,138 yards and six scores on the season, helping Buffalo to a shocking postseason berth with a 9-7 record.
Taylor was tended to by the team's medical staff on the field.
The Bills threw it on first down, resulting in an offensive pass interference penalty on receiver Kelvin Benjamin, who was covered by Ramsey. Bortles scrambled twice for first downs to get within field goal range for Josh Lambo, who connected from 44 yards with 2 seconds left.
As for the Jaguars, Sunday's playoff appearance is the first since 2007.