ATLANTA -- The Atlanta Falcons, like in the Super Bowl last season, couldn't hold a big halftime lead and it was the Miami Dolphins who came away with a victory this time.

Safety Reshad Jones intercepted Matt Ryan at the 6-yard line on a deflection with 39 seconds left and the Dolphins defeated the Falcons 20-17 on Sunday at Mercedes-Benz Stadium after trailing 17-0 at halftime.

"This was a huge win for us," said Jones, an eight-year veteran who played at the University of Georgia and is an Atlanta native. "Our defense has been playing great and it feels good to be a part of it. Now we just got to keep it going."

Cody Parkey kicked a decisive 39-yard field goal with 2:30 remaining after tying the game on a 49-yarder with eight minutes left that was set up by a bad snap on a Falcons punt.

Jay Cutler, who was 19 of 32 for 151 yards, threw two third-quarter touchdown passes for the Dolphins (3-2) and Jay Ajayi ran for 130 yards on 26 carries.

"This week was all about keeping our emotions in check and staying positive," Ajayi said. "We aren't a team that quits. We kept our foot to the pedal and didn't let up."

Cutler hit Kenny Stills with an 11-yard touchdown pass to cap a 75-yard drive following the second-half kickoff, then connected with Jarvis Landry from 7 yards out late in the third quarter to pull the Dolphins within three points.

The second touchdown drive, which covered 51 yards, was kept alive by a roughing the passer penalty on defensive tackle Grady Jarrett that nullified an interception by linebacker Deion Jones that would have been his second of the game.

"This one hurts, that's for sure," Falcons head coach Dan Quinn said. "It was a tale of two halves. For us to be the team we all want to be, we have to be better and do it consistently. That's what it comes down to."

The Falcons (3-2) drove from their 13 to the Dolphins' 26 after Parkey's tie-breaking field goal as Ryan completed 5 of 8 passes for 61 yards.

Ryan tried to hit Austin Hooper over the middle on the interception by Jones, but the ball was deflected by the second-year tight end and Miami cornerback Cordrea Tankersley.

"I just kept my eyes on the ball and was able to make the play," Jones said. "I'd cheated a little on the backside and just took off."

Atlanta scored on three of its first four possessions and seemed in control at halftime as Ryan completed 15 of 21 passes and the Falcons held a 233-140 edge in net yards.

Marvin Hall, elevated from the practice squad Saturday, hauled in a 40-yard bomb from Ryan late in the first quarter for his first NFL catch after Matt Bryant's 50-yard field goal on Atlanta's first possession.

Tevin Coleman had a 6-yard touchdown run in the second quarter set up by Devonta Freeman's 44-yard scamper.

Ryan, who was sacked twice, finished 24 of 35 for 248 yards. The interception was his sixth of the season after he threw just seven last season while being named NFL MVP.

Most of the interceptions have come on tipped balls.

"You've just got to cut loose and let the ball rip," Ryan said. "At some point, those balls are going to bounce our way."

NOTES: Dolphins C Mike Pouncey left the game in the second quarter and didn't return after being evaluated for a concussion. ... LB Vic Beasley Jr. (hamstring) and RT Ryan Schraeder (concussion) played for the first time since Sept. 17, and S Ricardo Allen (concussion) was back after missing one game, giving the Falcons three of their five previously injured starters. ... The Falcons were without WR Mohamed Sanu (hamstring) and DE Courtney Upshaw (ankle). ... RB Brian Hill, a fifth-round draft choice, was waived by the Falcons to clear a roster spot for WR Marvin Hall. ... WR DeVante Parker (ankle) was inactive for the Dolphins. ... TE Julius Thomas, WR Kenny Stills and S Michael Thomas were not on the Dolphins sideline during the national anthem. ... All of the Falcons stood for the national anthem. ... Mercedes-Benz Stadium's troublesome retractable roof was closed and will remain so for the rest of the season.