Johnson piled up 131 yards on 19 carries to offset a less-than-stellar day for Vince Young, who despite going only 12-for-25 for 173 yards through the air managed to hurl two touchdown passes.
His main target was Kenny Britt, who hauled down four passes for 86 yards and a touchdown as Tennessee (3-2) won for the third time in four games.
Dallas out-gained the Titans 511-321 in total yards but Stephen Tulloch, Alterraun Verner and Michael Griffin each picked off Cowboys signal-caller Tony Romo.
The picks marred an otherwise standout performance by Romo, who went 31-of-46 for 406 yards and three touchdowns for Dallas (1-3). Miles Austin grabbing nine passes for 166 yards and a score.