Substitute Dino Baggio made it a nerve jangling finish by heading home Brett Emerton's cross four minutes from the end to give Rovers hope, but Leeds held out.
Johnson was a revelation on the left flank and 34-year-old David Batty gave the midfield added bite against one of his old clubs in his first Premiership start for 18 months.
Blackburn have shown better form on their travels this season, but they were second best until it was too late.
Reid, given a vote of confidence by his bosses in midweek, had his name chanted repeatedly by Leeds fans and he should have been cheering three goals in the opening eight minutes.
All three chances were created by Mark Viduka, but first Alan Smith shot too high when well placed, then Jody Morris blazed high and wide and when Viduka's inventive overhead pass put him through again, Smith could only shoot past the foot of the left post from just inside the penalty box.
Leeds were eventually rewarded with their first goal in four Premiership games on 11 minutes and again Viduka played an important part.
Jermaine Pennant made the running on the right and from his pass Viduka tried a low curling shot which Brad Friedel could only parry.
Johnson was lurking just outside the six-yard box and made no mistake for his second goal since a £7m move from Derby two years ago.
The Leeds players, rightly pilloried for their abysmal showing at Everton, joined in a mass celebration which was repeated when Johnson scored his second in the 27th minute.
Pennant's header into the goalmouth was helped on by Blackburn defender Steven Reid's raised hand and Johnson, standing beyond the far post, rifled a stunning shot across Friedel into the net.
A minute after Johnson's second, the post denied Andy Cole with a shot on the turn which had Paul Robinson beaten.
Johnson went close to completing his hat-trick before Blackburn almost hit back again with David Thompson's 25-yarder and a curling 20-yard free-kick, both testing Robinson to the full.
Smith should have killed the game less than 30 seconds after the restart, but Friedel did enough to save his attempt to loft the ball over the American. Not one of Smithy's better days!
Baggio's late goal rewarded Blackburn's second-half improvement and there was further panic in the Leeds goalmouth before Uriah Rennie's final whistle.