The shock victory was made all the sweeter for Boro considering they had suffered a heartbreaking last-gasp defeat to their hosts in last season's fourth-round meeting.
Charles had been on target in January last year as a Shane Long goal eliminated the Broadhall Way outfit, but he made his first-half goal on Saturday count almost a year later to eliminate a toothless Reading side.
After a slow start, Stevenage first declared their intent in the 10th minute, Scott Laird heading just wide of goal following Luke Freeman's corner.
Graham Westley's men grew further into the game and took a deserved lead with 21 minutes played.
Laird was unchecked as he released Charles just outside of the box, the former Brentford striker shrugging off his marker to clip beyond Adam Federici's reach.
Jay Tabb threatened to respond immediately, but his left-footed effort sailed wide of the target.
It was to be the Royals only meaningful attempt on goal in the first half, with the visitors soon back in the driving seat.
Chris Beardsley was well-placed to double Boro's lead when Freeman swung in another tricky corner in the 28th minute, but he nodded tamely off target.
And with Reading struggling to contain their opponents before the break, Charles was given time and space to hook Lawrie Wilson's pinpoint cross wide of goal.
The interval allowed the hosts to regroup and somewhat dispel their early jitters, as Adam Le Fondre forced a dramatic save from Chris Day following the restart.
And a gilt-edged chance went begging in the 58th minute, Simon Church heading the ball into the path of the onrushing Michail Antonio, who sliced wide with only Day to beat.
Stevenage soon rallied, Mark Roberts catching the home backline unawares to feed Wilson, who could only warm Federici's palms.
With the final 20 minutes approaching, and with victory in sight, Westley instructed his charges to track back, thus minimising the Royals' counter-attacking threat.
Mathieu Manset's introduction for Le Fondre provided some much-needed attacking impetus in the Reading midfield, with some clever build-up play allowing Church another attempt on goal in the 68th minute.
The Wales international striker swivelled on the penalty spot to connect with Hal Robson-Kanu's cross but failed to worry Day with his wayward strike.
And the shock win was almost sewn up 10 minutes from time, Joel Byrom's dipping drive from 25 yards proving too hot to handle for Federici, who anxiously juggled the ball before smothering the danger.
Reading poured forward as they searched for the goal to keep their FA Cup dream alive, but Manset spurned an easy chance to grab an equaliser four minutes into injury time.