The Bulls were clinging to a tenuous 12-6 lead when the 29-year-old Welsh dual-code international forced his way over for the all-important try.
After losing the first round of his costly High Court battle with his former club Leeds this week, Harris will be consoled by an impressive overall performance in an otherwise undistinguished display by his team.
Bradford led 24-6 midway when Leon Pryce added a fourth try midway through the second half but they were twice reduced to 12 men, with Michael Withers and Stuart Reardon sent to the sin bin, and they were left to desperately hang on.
Bradford's teenage winger Karl Pryce and influential scrum-half Paul Deacon again found The Willows a happy hunting ground. Pryce anticipated Deacon's bouncing kick to score in the corner before Deacon cut between two static defenders for an individual effort inside the opening 11 minutes.
But the Bradford side of 2005 is far from the dominant one of recent years and the Bulls failed to put the game away as Salford recovered some composure.
With Malcolm Alker setting a captain's lead as usual, Salford began to threaten more on attack and got back in the game when Chris Charles was involved three times in a sustained attack that ended with Junior Langi's first try this season.
Salford: Fitzpatrick; Hodgson, Littler, Sibbit, Langi; Beverley, Robinson; Rutgerson, Alker, Stringer, Shipway, McAvoy, Charles. Substitutes used: Coley, Haggeraty, Baldwin, Hartley.
Bradford: Withers; Reardon, B Harris, Johnson, K Pryce; I Harris, Deacon; Vagana, Henderson, Fielden, Peacock, Meyers, Parker. Substitutes used: Hape, L Pryce, Lynch, Cook.
Referee: R Silverwood (Mirfield)Reuse content