Only two minutes on the clocka nd a lovely passing move led to the award of a penalty. Swift completed a perfect one-two with Andy Rinomhota on the edge of the area and he was barged over as he bore down on Dillon Phillips in the Addicks goal. George Puscas stepped up and slammed home, arrowing down the middle to make it 1-0 from the spot.
That goal seemed to spur the home side into action and a couple of good pieces of defending from former Athletic defender Michael Morrison preserved the Royals lead during a good spell for Lee Bowyer's men.
Ten minutes gone and captain Jason Pearce headed over from a deep cross from the right, but at the other end Swift floated a cross towards Meite at the end of a good period of possession for the visitors - this time the four-goal hero of last weekend couldn't rise high enough to direct the ball towards target.
Olise and Meite combined on a counter attack and the latter managed to dink a cross dangerously across the face of goal - but another man in blue and white couldn't arrive to apply the finishing touch.
Both teams were playing some nice stuff and Meite forced a save from Phillips as he connected with John Swift's corner, directing a header down into the ground and into the palms of the Charlton keeper on the bounce.
Meite had a better effort after the drinks break, attacking an arced ball from Swift once more but this time powering a header inches wide of the top left corner.
Charlton had a goal ruled out moments later, McGeady's low shot being palmed away by Rafael only for an offside Chucks Aneke to convert into the open net - but the flag was promptly raised to cut the home side's celebrations short.
Brilliant feet from the lively McGeady almost helped the hosts draw level soon after - the winger earning a yard on the right to cross into the near post where an unmarked Bonne cushioned a volley across the face of goal and just wide.
Aneke fell foul of the offside flag once more as he chested down a cross into the middle before forcing Rafael into a smart save to his left. But Reading had held firm and led at the interval.
Half-time | Charlton Athletic 0-1 Reading
Jordan Obita was brought on at the break to replace Pele but Charlton were on the front foot from the off and it took a good block to deny Aneke and deflect his shot over the bar.
Charlton continued to press for an equaliser but a very nice cross from substitute Omar Richards nearly picked out Sam Baldock in the middle on the hour mark.
Charlton were ramping up the pressure as we entered the final 20 minutes and a good run down the left from Doughty resulted in a cut back that nearly picked out a teammate. Reading eventually scrambled it clear.
And Osho conceded a free kick on the left side of the box which was whipped in but thankfully headed high and wide by Aneke at the back post.
At the other end, a neat turn from Meite on the right led to a low cross which Richards battled to get on the end of but the ball was eventually swept up by Phillips.
Substitute Forster-Caskey bundled his way into the box with six minutes left and appeals for a penalty were waved away as he wrestled with Obita inside the area.
And Charlton's frustration grew and grew as time ticked away and the Reading defence held firm.
Rafael gobbled up a cross from Matthews at the start of seven minutes of added time and Cullen scurried forward only to scoop an effort harmlessly over the crossbar.
The Addicks threw everything at us in the final few minutes, but Reading's resilience was strong for all to see and three points headed back to Berkshire.
Full-time | Charlton Athletic 0-1 Reading
Charlton Athletic: Phillips, Pearce (c), Pratley (Forster-Caskey 84), Bonne, Matthews, Lockyer, Cullen, Aneke, Oshilaja (Doughty HT), Morgan (Williams HT), McGeady (Hemed 79).
Unused subs: Amos, Purrington, Sarr, Field, Oztumer.
Yellow: Doughty, Cullen, Phillips.
Reading: Rafael, Osho (Gunter 75), Blackett, Morrison, McIntyre, Rinomhota, Pelé (Obita HT), Swift (c) (Moore 75), Méïté, Olise (Richards 61), Pușcaș (Baldock 56).
Unused subs: Walker, Miazga, McCleary, Boyé.
Goals: Puscas pen (3)
Yellow: Blackett, Osho, Baldock.
Referee: Mr D Bond