The Bills, who snapped a two-game losing streak with a one-point win at Washington engineered late by Edwards, are in the thick of the AFC wild-card playoff race. Buffalo is right behind Jacksonville (8-4), Cleveland (7-5) and Tennessee (7-5) and play at the Browns next week.
Meanwhile, Miami is still trying to avoid becoming the first team in NFL history to go 0-16.
Beck will be making his fourth start since replacing Cleo Lemon and is coming off his poorest game, a mistake-filled 40-13 home loss to the New York Jets in which he accounted for five turnovers.
Since Kelly and Marino left the scene many years ago, the Bills and Dolphins have been trying to find consistency at the quarterback position. Each club has run through starter after starter, the main reason this once-heated rivalry barely simmers now.
But Edwards, a third-round pick out of Stanford, and Beck, a second-round choice out of BYU, offer hope. Each is known for playing an intelligent game of football and the two are familiar with one another from their college days in the Pac-10. Edwards remembers winning at BYU 18-14 in a game he threw three interceptions but rushed for one.
"I don't think we ever started against each other so this will kind of be the first time for us," he said of himself and Beck. "We developed a relationship through the (scouting) combine and the (NFL) Rookie Premiere and offseason workouts and everything. It's another game and I'm just excited to get back out there again."
Edwards, who has made five starts this season (4-1 record), has learned quickly that professional football can be a cold business and in the era of free agency, head coaches don't have the patience they once did with their quarterbacks.
J.P. Losman, a former first-round pick of the Bills, lost his starting job to Edwards due to an injury then lost it a second time this season based on performance. After making four starts, Edwards watched from the sidelines for a month after he suffered a badly sprained right throwing wrist, not knowing if he'd ever get the chance to play again.
"It's not like the college level where you're kind of the guy for the entire season and they're going to run with you the entire season," said Edwards, who is 102 of 157 for 1,047 yards, one touchdown, five interceptions and a 72.9 rating. "It's so much more of a what-have-you-done-for-me-lately business and that you always have to be prepared each week. Regardless of whether you're second or third string, that's something I'm starting to realize. The sooner you accept all of that, the sooner you'll be able to get things done out there."
Edwards got it done in last Sunday's 17-16 win over Washington, completing some clutch throws down the stretch, including a 30-yard laser to Josh Reed in the final 30 seconds that set up placekicker Rian Lindell for the winning field goal.
While it hasn't been flashy, Edwards is the first Bills rookie quarterback since Joe Ferguson (nine) in 1973 to win at least four games. Coach Dick Jauron liked the fact that Edwards came through at crunch time last week.
"What he does, doesn't surprise you by the nature of how he practices," Jauron said. "He doesn't seem to rattle, he likes being out there. This should help him as we move on. He's taking the end-of-the-game situation, where we've been behind, and got us into position for a chance to win. It's big."
Beck, on the other hand, put the Dolphins into a position to lose against the Jets and that's just what occurred. His three interceptions and two fumbles fueled the Jets -- they scored the game's final 30 points -- 16 of them off the turnovers.
"Offensively, it was difficult to go out there and have a performance like that, especially for me because I consider one of the strengths of my game is taking care of the football," Beck said. "It hurts because you want to go out there and win."
At BYU, Beck threw for more than 11,000 yards with 79 touchdowns and 38 interceptions. So far this season, he's 46 of 84 for 418 yards, zero TDs, three interceptions and a 53.6 rating. Beyond the statistics that suggest a lot of growing pains, Beck is carrying the burden of Miami's horrific record. The offense hasn't scored a touchdown in three consecutive games, the first time that's occurred in team history. It's an offense missing running back Ronnie Brown (injured reserve), receiver Chris Chambers (traded) and running back Ricky Williams, whose comeback from an NFL suspension lasted one game as he injured a shoulder.
Miami has lost six games by three points, including the November game against the Bills when the Dolphins dominated statistically but still found a way to lose.
"We have to fight," Beck said. "I mean shoot, in boxing you're going to get popped in the face, that doesn't mean that you're going to lose the fight just because you get hit a few times. We've got fighters on this football team and that's what we have to be, we each have to be fighters right now and we're taking a lot of shots to the face and getting knocked down, but we're going to have (to) get back up and then throw our punches."
The Bills know they can't afford to look past the desperate Dolphins and ahead to the Cleveland game. Jauron has done a good job keeping his team focused after dealing with more than its share of serious injuries, lineup changes and heartbreaking losses to somehow cobble together a .500 record with a month to play.
"We pictured better," said Jauron, who can win his 50th career game on Sunday.
"I'm a big believer in that you have to believe or nobody else will. If we as coaches don't believe, why would the players? As a group we had faith. We know how hard it is to win a game on Sunday in this league for most of us. Obviously, some teams in this league are winning pretty easily on Sundays but for most of us, it's difficult every week."
And what of Miami?
"They're certainly capable of beating anybody, and we are too," Jauron said. "We generally play close and we have to find a way to win them at the end. You've got to play hard, you've got to play well and you've got to get a little lucky."