Jones-Drew, who totaled 70 yards rushing, scored on runs of 6, 1 and 8 yards, all in the second quarter.
David Garrard was 18-for-27 passing with two touchdowns for the Jaguars (4-5).
Jacksonville's Fred Taylor added 80 yards on 18 carries.
Daunte Culpepper, who signed a two-year-contract Tuesday with the Lions (0-9), started and completed 5-of-10 passes for 104 yards, with an interception.
Drew Standon followed, completing 6-of-8 passes for 94 yards and a score.
The Lions have lost 10 in a row going back to last season and are the only winless team in the NFL this year.