NFL round-up: Dolphins secure play-off spot as Lions clinch NFC North
The Detroit Lions also secured a postseason spot after clinching the NFC North with a victory over the Minnesota Vikings, while the Seattle Seahawks' late win over the Tennessee Titans kept their season alive.
Quarterback Joe Flacco continued his remarkable late-career comeback in the NFL as he led AFC play-off hopefuls the Cleveland Browns to their third straight win with a 36-22 victory at the Houston Texans.
Miami becomes the second team in the AFC to secure a play-off place, following the Baltimore Ravens, but they were pushed to the brink by Dallas and their quarterback Dak Prescott.
After a gruelling, physical encounter, Dallas got in front with a touchdown with just 3:27 left in the game after Prescott led an outstanding 17 play, 69-yard drive which culminated in a brilliant touchdown catch in the corner, under intense pressure from Brandin Cooks.
But Miami quarterback Tua Tagovailoa responded in kind, managing the clock perfectly as he led Miami down the field with a 64-yard, 12-play drive to set up Sanders.
Sanders, who made all five of his field goal attempts including three from over 50 yards, made no mistake from 29 yards to seal a crucial victory over a Dallas side that had already grabbed a spot in the NFC's play-offs.
"I think the key was the guys just having competitive greatness," said Tagovailoa.
"The defence did a great job, the offence did a great job, this is a great team and this is a great team win. It was a team win," he said.
Elsewhere, the Detroit Lions clinched their first division title since 1993 as they secured the top spot in the NFC North with a 30-24 win over the Minnesota Vikings.
Jahmyr Gibbs had two rushing touchdowns for the Lions, the second coming early in the fourth quarter, but victory was only clinched with just 49 seconds left, when Ifeatu Melifonwu intercepted a pass from Vikings quarterback Nick Mullens - the Lions' fourth pick of the game.
The Seattle Seahawks, fresh from their thrilling Monday night win over the Philadelphia Eagles, further boosted their NFC play-off chances with a 20-17 win at Tennessee.
Seattle (8-7) trailed 17-13 in the final minute of the game before Colby Parkinson pulled in a brilliant catch from a 5-yard pass from Geno Smith to win the game.
Flacco back to his best
The Browns meanwhile turned to Flacco, a 38-year-old who was without a team at the start of the season, as their fourth quarterback in an injury-plagued year earlier this month, and he has kept them on track for a postseason berth.
He looked back to his very best on Sunday as he threw for three touchdowns and 368 yards in a win which took the Browns to a 10-5 record in the AFC.
It was also a stellar day for his favoured target, receiver Amari Cooper, who had two touchdowns and put up 265 yards on 11 receptions, the most receiving yards in a game this season and a franchise record.
Flacco, a Super Bowl winner with Baltimore in 2012, was released by the New York Jets in the off-season and his career looked to be over until his unexpected return.
After a four-yard rushing touchdown from Jerome Ford set the Browns on their way, Flacco found Cooper wide left and the receiver raced into the end-zone for a 75-yard score.
The Texans responded immediately though, with Dameon Pierce showing his speed, power and agility as he returned the kick-off for a 98-yard touchdown.
Dustin Hopkins pulled his hamstring chasing Pierce, leaving Cleveland without a field goal kicker for the remainder of the game.
But the inspired Flacco delivered a magnificent throw to find David Njoku in the end-zone with a 21-yard pass to ensure Cleveland went up 22-7 at the break.
The game was put beyond Houston's reach when Flacco again connected with Cooper on a seven-yard pass and, at the start of the fourth, Kareem Hunt ran in from a yard to make it 36-7.
Meanwhile, the Indianapolis Colts' postseason hopes suffered a blow with a 29-10 loss at the Atlanta Falcons.
Recalled quarterback Taylor Heinicke avoided the turnovers that have hampered Atlanta this year as he threw for 229 yards and a touchdown to keep the season alive for the 7-8 Falcons.
The Jacksonville Jaguars are fading out of contention in the AFC after suffering their fourth straight loss with a 30-12 defeat at the Tampa Bay Buccaneers.