Jones-Drew finished with 136 total yards, including 85 on the ground against one of the league's worst run defenses.
Tampa Bay's bigger problem in its seventh consecutive loss was turnovers.
The Buccaneers (4-9) had seven of them, helping set up each of Jacksonville's four touchdowns in the second quarter. The Jaguars (4-9), who hadn't scored more than 20 points all season, scored four times in a span of 7:32. They scored on offense, defense and special teams in the same game for the first time since Nov. 1, 1998, at Baltimore.
That also was the last time Jacksonville had scored 28 points in a quarter.
Josh Freeman and Preston Parker had a lot to do with Jacksonville's latest scoring frenzy.
Freeman, back after missing last week's game against Carolina because of an injured throwing shoulder, threw two interceptions and fumbled near the goal line. He completed 16 of 30 passes for 181 yards and was benched late in favor of Josh Johnson.
Parker's day was nearly as bad. He fumbled two punts, both caused by special teams ace Montell Owens, and had a costly penalty. Colin Cloherty, signed off the practice squad Friday, scooped Parker's second fumble and returned it 4 yards to give the Jaguars a spark.
Blaine Gabbert found Marcedes Lewis behind the defense for a 62-yard gain on the next drive, setting up Jones-Drew's 1-yard score that tied the game at 14.
Two plays later after Parker was flagged for holding Freeman fumbled at the 1-yard line as Daryl Smith sacked him. Nate Collins recovered in the end zone to make it 21-14.
Freeman threw an interception on Tampa Bay's next possession. Jacksonville turned the short field into a 28-14 lead when Gabbert found Jones-Drew with a short pass near the goal line. Drew stretched the ball over the pylon for his 71st touchdown in 90 career games, breaking the team record held by Fred Taylor.
Jones-Drew didn't celebrate. Instead, he simply jogged back to the bench with the record-setting football.
He wasn't done, either.
The player Bucs coach Raheem Morris dubbed a "rolling ball of butcher knives" earlier in the week made it 35-14 in the fourth when he caught a short pass near the goal line and plowed through two defenders for another score. He also scored from a yard out late.
Gabbert completed 19 of 33 passes for 217 yards, with two touchdowns and two interceptions.
The only downside for Jacksonville, which ended a three-game slide, was injuries. The Jaguars lost receivers Mike Thomas (concussion) and Cecil Shorts (hamstring) and place-kicker Josh Scobee (leg) during the game.
Scobee's injury forced the team to go for a fourth-and-9 play late in the game and also attempt a 2-point conversion after Jones-Drew's fourth touchdown.
Linebacker Russell Allen had to kick off, providing some levity in a blowout. It looked more like an onside kick than anything.
When the final seconds ticked off the clock, the Jaguars had even more fun by dosing Tucker with ice water. Tampa Bay 14, Jacksonville 41
Tampa Bay 7 7 0 0 14
Jacksonville 0 28 0 13 41
TB • Blount 1 run (Barth kick), 9:24.
TB • Freeman 13 run (Barth kick), 14:09.
Jac • Cloherty fumble recovery in end zone (Scobee kick), 7:36.
Jac • Jones-Drew 1 run (Scobee kick), 2:05.
Jac • Collins fumble recovery in end zone (Scobee kick), 1:53.
Jac • Jones-Drew 5 pass from Gabbert (Scobee kick), :04.
Jac • Jones-Drew 5 pass from Gabbert (Scobee kick), 10:22.
Jac • Jones-Drew 1 run (run failed), 2:31.
Attendance • 62,562.
First downs 15 21
Total Net Yards 280 325
Rushes-yards 24-110 33-116
Passing 170 209
Punt Returns 4-(-2) 1-5
Kickoff Returns 1-0 1-19
Interceptions Ret. 2-12 3-14
Comp-Att-Int 17-32-3 19-33-2
Sacked-Yards Lost 3-14 1-8
Punts 5-37.8 7-41.4
Fumbles-Lost 6-4 2-0
Penalties-yards 12-97 8-80
Time of Possession 27:11 32:49
Rushing • Tampa Bay, Blount 18-74, Freeman 4-26, Madu 1-6, Lumpkin 1-4. Jacksonville, Jones-Drew 27-85, D.Harris 1-24, Bolen 1-10, Gabbert 4-(minus 3).
Passing • Tampa Bay, Freeman 16-30-2-181, J.Johnson 1-2-1-3. Jacksonville, Gabbert 19-33-2-217.
Receiving • Tampa Bay, Parker 3-35, Williams 3-35, Briscoe 3-20, Winslow 2-38, Lumpkin 2-18, Lorig 1-22, Benn 1-7, Blount 1-6, Madu 1-3. Jacksonville, Jones-Drew 6-51, Dillard 5-45, Osgood 3-23, Lewis 2-77, West 2-19, Thomas 1-2.
Missed Field Goals • None.