Wolves boss Mick McCarthy must think he got away with daylight robbery after he snapped up the American striker for just £100,000 from Blackburn Rovers.
The 22-year-old scored the winner on his debut at Burnley last weekend and followed it up with another clinical finish in the 47th minute to sink Luton.
Johnson's touch of class was the difference between the sides as both teams were guilty of missing golden chances.
Rowan Vine and Warren Feeney were both full of energy for Luton but the cutting edge was missing as Mike Newell's side slipped to their second defeat of the season.
Even the second-half introduction of new signing Sam Parkin, who made his debut following his £340,000 arrival from Ipswich Town, could not inspire the visitors to salvage a point.
Parkin showed enough to prove he will be a useful capture and was unlucky not to grab an equaliser three minutes from time when his low shot whistled just wide.
Luton then knew it would not be their day in stoppage time when Carlos Edwards was inches wide with a fierce volley.
A combination of poor finishing and goalkeeper Marlon Beresford prevented Wolves establishing a healthy advantage before half-time.
Before Wolves launched their flurry, Luton had chances of their own to take control of the game.
Vine, who was consistently Luton's most potent threat, was denied by goalkeeper Matt Murray, before Carlos Edwards shot into the side-netting after a neat piece of skill.
Karl Henry then gave a sign of the pressure that was to come from the hosts when Beresford parried his 26th-minute shot.
Wolves created three clear openings in the space of little more than 60 seconds, only to squander all three.
Johnson lifted his close-range shot over the bar in the 38th minute, Carl Cort failed to hit the target with a close-range header and Seyi Olofinjana was denied by Beresford.
Unfortunately for Luton, Johnson found his shooting boots at the start of the second-half and the result was impressive.
Gary Breen fired a hopeful throughball upfield that Luton skipper Steve Robinson inadvertently flicked into the path of Johnson.
Johnson took a couple of paces forward before rifling a low left-foot drive that whistled past the outstretched hand of Beresford.