Johnson claimed the first on the half-hour when he raced onto a through-ball from Jamie McMaster and slipped the ball past Carl Muggleton.
McMaster himself added a superb second ten minutes later following a neat one-two on the edge of the box with Johnson bending his shot into the top right hand corner of the net from the edge of the area.
United managed to control the first half by keeping the ball on the ground and playing a neat passing game. Two-nil at half time and there could be no complaints from Steve Agnew and the bench at an excellent performance.
The United side included former Doncaster Rovers midfielder Andy Watson, given a trial by Peter Reid after he was released by Rovers, and he lasted 45 minutes before he made way in the second half for Aaron Lennon.
Mark Allott and Glyn Hurst both wasted chances to pull one back before the break but the home side finally broke through on 51 minutes.
It was Allott who grabbed the goal when his side footed shot was blocked by Dominic Krief on the line but the ball spun up into the air and he followed up with a header to make it 2-1.
With 12 minutes left on the clock the small band of United fans saw exactly what all the hype concerning 16-year-old Aaron Lennon is all about.
The winger's jinxing run saw him beat at least two men before he set Simon Johnson off on another goalscoring opportunity, except this time Johnson's curling shot hit the foot of the post and rebounded to safety.
The game lost some of its momentum as both sides made a flurry of substitutions in the second half. Chesterfield finished the stronger of the two sides with Hurst having a goal disallowed by the referee.
David Reeves and Andy Rushbury both missed good chances late on but the Leeds youngsters held on for their first pre-season victory.
Chesterfield: Muggleton, Uhlenbeek, Payne, Blatherwick, O'Hare, Davies, Evatt, Hudson, Brandon, Hurst, Allott.
United: Carson, McStay, Richardson, Krief, McDaid, Watson, Keegan, McPhail, Okon, Simon Johnson, McMaster. Subs: Allaway, Gray, Woods, Constable, Shields, Lennon.