Johnson struck his first goal in 12 matches to put David Moyes' side in control and then teed up the second for James McFadden.
Everton nearly made the perfect start but Johnson was denied by the legs of Marcus Hahnemann within the opening two minutes.
Ibrahima Sonko was then required to come to his side's rescue, outmuscling McFadden after the striker had been allowed to run clear following Ivar Ingimarsson's error.
And it was no surprise when the visitors went in front on 14 minutes. Mikel Arteta spun away from Nicky Shorey and sent over a low cross from the right towards Johnson, who was allowed too much time to turn and hit a shot that deflected off Sonko and beyond the reach of Hahnemann.
The Reading keeper then reacted well to push away Leon Osman's flicked header from a free-kick after Johnson had been hurt in a clash of heads with Sonko.
And Osman then wasted a glorious chance to double the lead when he spun away from Sonko, but screwed his left-foot shot well wide with the goal gaping.
But the little midfielder was desperately unlucky not to score his second goal of the season midway through the half, when McFadden set him up for a drive that deflect off Ingimarsson and on to the underside of the crossbar before bouncing back up off the goal-line.
Reading's chances were few and far between, though Glen Little was denied a clear shot at goal by Simon Davies' last-ditch challenge after Kevin Doyle had been sent through by Stephen Hunt's chip.
But the home side were controversially denied a lifeline on the stroke of half-time when Gary Naysmith hauled down Seol as the South Korean striker spun into the penalty area.
Whether the challenge was in or out of the area will be debated long and hard, but it was a clear foul and Reading would have felt hard done to by referee Steve Tanner waving away their appeals.
A Reading equaliser then would have given the game a whole new outlook, but instead Everton put some daylight between themselves and their hosts with a second goal in the opening minutes of the second half.
Johnson was allowed plenty of time again down the left and outstripped the struggling Ingimarsson, before setting up McFadden, who easily turned Reading captain Graeme Murty before ramming home a close-range shot.
Reading responded by throwing on striker Leroy Lita for the ineffective Seol and the former England Under-21 striker soon saw a shot on the turn saved by Tim Howard.
Reading should have pulled one back when Lita headed down at the far post, only for James Harper to snatch at his shot and hit the ball wildly over the bar.
Howard then made a fine reaction save to palm away Doyle's low drive after Lita again had set him up and he was forced into action again with five minutes left, reacting well to push away Steve Sidwell's shot on the run.