Sam Ficken kicked a 44-yard field goal on the last play of regulation to give the Jets a 22-21 victory and end the Dolphins' four-game winning streak in the series.
The kick came after Sanders gave the Dolphins a 21-19 lead with his seventh field goal, a 37-yard kick that broke the previous mark of six set in 1999 by Olindo Mare against the New England Patriots.
Sanders also made field goals of 22, 25, 28, 31, 53 and 47 yards to account for all the Dolphins scoring.
Fitzpatrick, meanwhile, set a franchise single-game rushing record for quarterbacks with 65 yards on eight rushing attempts. The previous mark was 59 yards and belonged to Chad Henne, who did it in the 2011 Monday night season opener against New England.
Ficken's winning kick capped a 49-yard drive that included a key replay overturn of an incomplete pass. After rookie linebacker Andrew Van Ginkel recorded his first career sack to put the Jets in a third-and-17 from the Miami 45, cornerback Nik Needham broke up a pass intended for Vyncint Smith.
As the Jets lined up for their fourth-and-17, play was stopped for a review for possible defensive pass interference, and that was the final ruling, making it first-and-10 from the Dolphins 38.
Three plays later, Ficken gave the Jets the victory.
Perhaps the biggest factor in the loss for the Dolphins was the inability to convert in the red zone.
After coming in scoring touchdowns on 80 percent of their red-zone trips over the previous eight games, the Dolphins were 0-for-5 against the Jets.
After wide receivers DeVante Parker and Albert Wilson left the game with concussions, Isaiah Ford stepped up for the passing game. Ford came into the game with two career receptions before having six catches for 92 yards against the Jets.
The game-winning field goal represented the fifth lead change of the fourth quarter, as the teams traded five field goals.
The Jets scored the only two touchdowns on passes by Sam Darnold, one to Robby Anderson and the other Demaryius Thomas.
Thanks to Fitzpatrick's contributions, the Dolphins had a season-high 118 rushing yards, topping the 109 they had at Buffalo on Oct. 17.
Each team came up with a takeaway, with safety Steven Parker recording his second interception of the season for the Dolphins.
The Dolphins took a 3-0 lead after an impressive 15-play, 92-yard drive. The drive featured three third-down conversions, including one on a facemask penalty on Jets rookie Quinnen Williams and later on a 14-yard completion to Allen Hurns on third-and-10.
After the Jets took a 6-3 lead on Darnold's touchdown pass to Robby Anderson, they increased their lead to 9-3 after cornerback Nate Hairston interception Fitzpatrick.
The Dolphins answered with Sanders' second field goal, which capped a 67-yard drive. The big play on the drive was a 21-yard completion to Parker, but he left the game after that play to be evaluated for a concussion.
The Jets answered with their second touchdown, which came after the officials overturned a ruling of an incomplete pass after cornerback Nik Needham dislodged the ball from Demaryius Thomas as Thomas was falling into the end zone.
Fitzpatrick's running highlighted the Dolphins' two-minute drive, which ended with Sanders' third field goal.
After a 16-yard completion to Allen Hurns, Fitzpatrick had scrambles of 20, 16 and 6 yards. On his 16-yard run, he lateraled to tight end Clive Walford before being tackled to the ground and Walford picked up an additional 4 yards.
Sanders' fourth field goal accounted for the only points of the third quarter before the back-and-forth fourth quarter.
The Dolphins (3-10) will be back at MetLife Stadium next Sunday to face the New York Giants.