Johnson, who spent last season on loan at the Alexandra Stadium, pounced two minutes after replacing the injured David Graham to give the Bantams an interval lead.
When Jermaine Johnson flung across the ball, Lee Holmes headed back across the six-yard box allowing Johnson to volley home.
Then he latched onto another pass from his namesake to drill the third under home keeper Ben Williams after Marc Bridge-Wilkinson's shot had made it 2-0 early in the second-half.
The comfortable win was no more than the Bantams deserved for their control of most of the first-half. And while Crewe improved measurably when the game was lost and laid siege to the visitors there best chances had come and gone in the first 45.
Bradford came close in the first minute when Dean Windass got behind a static defence but half-hit his effort at Williams.
Colin Todd's side exhibited crisp passing and movement strangely lacking from the Railwayman who are taking some time to adjust to League One football after relegation.
Mike Higdon headed an early chance well over and teenager Michael O'Connor's powerful and accurate free kick produced a great save from Jamaican international keeper Donovan Ricketts.
But when Lee Holmes played in Johnson the winger went past O'Connor easily before flicking a low shot inches wide of Williams's near post.
Luke Rodgers spurned Crewe's clearest openings when he billowed the side-netting with a close range shot.
But it was Johnson who rammed the jeers back down the home crowd's throats in the 43rd minute after replacing the injured Graham.
When Jermaine Johnson was given too much time again to deliver a deep cross, Holmes headed the ball back across the six-yard box and the former Manchester United youngster was the quickest to react, moving in to volley home with his left peg.
As the booing died down, David Vaughan came close to a swift equaliser as he danced through into the box, first seeing Ricketts block off his route and then watching as his follow-up from the right of goal was cleared off the line by Nathan Doyle.
Things got worse for Crewe in the 52nd minute when Holmes moved away from Jon Otsemobor and flung a decent cross over the box, which was headed into space intelligently by Windass for Bridge-Wilkinson to move in and drill the ball into the bottom corner from 12 yards.
Vaughan looped the ball over to the back stick as Crewe tried to respond immediately, but Lowe's volley was from the acutest of angles and ended up in Rickett's mid-rift.
And Bradford sealed their win as early as the 57th minute when Jermaine Johnson teased and taunted before sliding ball in for Eddie Johnson to control and ram under Williams's body for the third.