Stevenage, beaten by Reading in the fourth round last year, took the lead when Charles fired past Adam Federici from the edge of the area.
Michail Antonio wasted a good chance to draw Reading level after the break as he sliced wide.
And Stevenage could have doubled their advantage when Joel Byrom's shot was tipped over by Federici.
Graham Westley's Stevenage went into the game on a run of just one defeat in the last 14 matches in all competitions, and started in confident mood.
Scott Laird had the first chance of the afternoon when he headed Luke Freeman's corner wide.
The impressive Laird was involved in the decisive goal. His run from midfield was unchecked and he released Charles, who was able to shrug off his marker to clip beyond Federici.
Reading rallied briefly, with midfielder Jay Tabb sending a left-footed effort wide.
But Brian McDermott's Championship side lacked spark throughout, and could have fallen further behind when, from another tricky Freeman corner, Chris Beardsley nodded tamely off target.
The Royals improved slightly as the second half began, with striker Adam Le Fondre forcing a dramatic save from Chris Day in the Stevenage goal.
A clear chance went begging when Wales international Simon Church headed into the path of the onrushing Antonio, who sliced wide with only Day to beat.
Stevenage, who beat Newcastle in the third round last season, went close to a second when Joel Byrom's dipping drive from 25 yards was juggled, then smothered, by Federici.
Reading poured forward as they searched for an equaliser but substitute Mathieu Manset fired wide in stoppage time.
Reading manager Brian McDermott:
"Stevenage are organised, with a fantastic manager who has done a terrific job. They deserved to win. We were a little bit too nice today. We had to win more tackles and more second balls.
"You can have times when players don't play to their level as individuals but today we didn't perform as a unit. For me it should have been a 0-0 game.
"We have reached the quarter-finals of the FA Cup in the past couple of years and we wanted a good run again this season.
"Our energy levels were not good enough and we didn't move the ball well. I have been disappointed in our performance in the last couple of games and all we can do is move on quickly."
Stevenage boss Graham Westley:
"There have been rumours that I was moving on all week. Everyone keeps asking me if this is my last game for the club.
"I just focus on the games. If the club comes to me and says there has been an approach I will deal with it.
"Today this was the right performance. It was about coming here and stopping them playing. We had to stop their attacking assets. I think our lads were energetic and athletic as they always are.
"People talk about the FA Cup falling back in the pecking order but it still has magic for me. In the old days it was a really big day."
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