Jones, who came in with just one touchdown, caught 12 passes for 253 yards and two scores as the Falcons won their third game in a row, beating the Bucs 34-20.
Jones teamed with fellow wide receiver Mohamed Sanu for a 51-yard touchdown on a trick play and caught a 25-yard TD pass from quarterback Matt Ryan, who finished 26 of 35 for 317 yards and two scores.
The victory for the Falcons (7-4) snapped a two-game winning streak by the Buccaneers (4-7).
Jones has 80 catches for 1,359 yards and 10 touchdowns in 11 career games against the Buccaneers.
Sanu's bomb to Jones out of the wildcat formation early in the second quarter to break a 3-3 tie was the six-year veteran's third NFL touchdown pass. Sanu botched a fake handoff to Tevin Coleman, but regained control of the ball and hit Jones in the end zone.
Ryan extended his streak with at least one touchdown to 30 games on his connection with Jones in the second quarter that helped put the Falcons up 20-6 at halftime.
Jones had six catches for 138 yards in the first half.
Matt Bryant had two first-half field goals for the Falcons, hitting from 49 and 36 yards, while Patrick Murray connected from 36 and 27 yards for the Buccaneers.
The Falcons drove 78 yards after the second-half kickoff and went up by 21 points on Coleman's 3-yard touchdown before the Bucs rallied.
Running back Peyton Barber scored from 2 yards out in the third quarter and a yard out early in the fourth, both capping long drives.
The Bucs drove to the Falcons 19 after a 37-yard return by Brett Grimes following a fumble by Terron Ward killed a long drive, but safety Keanu Neal knocked away a fourth-and-1 pass by Ryan Fitzpatrick with seven minutes remaining.
Coleman's second touchdown run, from 14 yards out, clinched the Falcons victory with just under two minutes remaining. Coleman finished with 97 yards rushing on 19 carries.
Fitzpatrick completed 27-of-44 passes for 283 yards. Neither Ryan nor Ryan had an interception.
NOTES: The Falcons lost CBs Desmond Trufant (concussion) and Brian Poole (lower back) in the second quarter. ... The Bucs had RT Demar Dotson and C Ali Marpet leave with knee injuries and RB Doug Martin suffer a concussion, all in the second quarter. ... DT Clinton McDonald (back), S T.J. Ward (concussion) and CB Josh Robinson (hamstring) were hurt in the third quarter. ... In addition to QB Jameis Winston (shoulder), the Bucs started the game without DE Robert Ayers (concussion), CB Vernon Hargreaves (hamstring) and G Evan Smith (concussion). ... Falcons RB Devonta Freeman (concussion) missed his second straight game. ... Two remaining end sections of the Georgia Dome, which was imploded Monday, tower over rumble next door to Mercedes-Benz Stadium. ... The Falcons and Bucs play in Tampa on Dec. 18. ... The Falcons host Minnesota next Sunday in their only remaining game not against an NFC South opponent. ... The Bucs are at Green Bay next Sunday in their third straight road game.