ALBION set up an FA Cup fourth-round trip to Peterborough on Saturday week thanks to a nail-biting 4-3 penalty shootout success.
On-fire Roman Bednar rammed home the decisive tenth spot-kick to settle this strength-sapping replay which went all the way.
Bednar and James Morrison had earlier both scored for the second successive game, in the 14th and 51st minutes respectively, to put Albion in firm control.
But Addicks midfielder Darren Ambrose pulled one back in the 64th minute and sub Chris Dickson took the tie into extra-time by clawing the Londoners level in the first minute of stoppage time.
After a scoreless extra 30 minutes, Charlton striker Luke Varney and Baggies skipper Jonathan Greening both missed penalties before ex-Addicks keeper Dean Kiely handed Albion the advantage by keeping out Zheng Zhi.
And Bednar fired Albion through by converting their fifth penalty in front of the Smethwick End.
The promotion-rivals hadn't met in the cup for 18 years before the first tie at the Valley ten days ago but tonight locked horns for the third time in a month.
Seven points separated leaders Albion from fifth-placed Charlton in the Championship but it was a place in the final 32, and not points, on both teams' minds at The Hawthorns.
Tony Mowbray rang four changes as Martin Albrechtsen, Zoltan Gera, Filipe Teixeira and Bednar came in for Paul Robinson (suspension), Kevin Phillips - rested altogether - and benched duo Robert Koren and Chris Brunt.
Charlton counterpart Alan Pardew named the same team for the third successive match.
Chances were few and far between during the early exchanges, with wayward long-range shots from Gera and Izale McLeod the only efforts on goal in the first ten minutes.
But, completely out of the blue, Albion snatched a 14th-minute lead.
Greening left Varney for dead as he controlled Gera's throw-in and raced to the byline.
The Albion captain picked out Teixeira at the far post whose header back across the face of goal was poked home by the unmarked Bednar - his ninth goal in just 11 appearances.
The breakthrough sparked an upturn in goalmouth action and, after a brief spell of Baggies pressure, Charlton produced their most positive moment to date in the 21st minute.
Ambrose's deflected shot fell kindly for McLeod on the right-hand edge of the Albion box and it needed an important block by Leon Barnett to divert the ex-MK Dons marksman's fierce drive over.
McLeod had an even better chance moments later but fired Varney's knockdown straight at Kiely from 15 yards.
The Addicks striker should have done much better in the 26th minute when Varney's flick-on put him clear of the Baggies defence.
However, McLeod produced an air shot as he bore down on goal, allowing the on-rushing Kiely to gather the ball.
Ishmael Miller recorded Albion's next effort on goal in the 35th minute when he collected Carl Hoefkens' neat pass, spun Matt Holland and curled wide from 20 yards.
Albion threatened again moments later when Barnett's ball over the top freed Bednar down the left. Only Paddy McCarthy's last-ditch interception prevented strike-partner Miller tapping home the Czech international's unselfish low cross.
From the ensuing corner, Morrison saw a 20-yard rocket whistle just past the near post after Varney had only partially cleared Greening's centre.
The Albion pressure continued when Albrechtsen should have done much with a free header, which flew well wide, from Teixeira's dangerous centre.
But Albion had a real let off in first-half stoppage time.
Pele dallied too long on the ball and was dispossessed by the busy McLeod who raced into the box and squared to the unmarked Varney.
With just Kiely to beat, the ex-Crewe striker controlled the ball before inexplicably firing over from eight yards.
In keeping with its predecessor, the second period took a while to get going - until Morrison made it 2-0 in the 51st minute.
The former Middlesbrough midfielder controlled Teixeira's square ball before firing into the bottom left-hand corner from 20 yards, giving Addicks keeper Nicky Weaver no chance.
Albion were suddenly in full flow and a great move involving Morrison, Hoefkens and Bednar set up a half-chance for Gera, who tested Weaver with a stinging 18-yard drive.
But after another lull in the game, Charlton pulled one back in the 64th minute.
Kiely rushed off his line to slide in and prevent sub Chris Iwelumo getting on the end of Ambrose's through-pass.
But the ball rebounded straight back to Ambrose who tapped it into the unguarded net.
Back came Albion and Gera fizzed a 30-yard pile-driver just over Weaver's bar.
But the Addicks almost drew level in the 68th minute when only Albrechtsen's last-ditch near-post block prevented Lloyd Sam converting Varney's low cross.
Albion survived another scare moments later when successive blocks from Kiely, Greening and Pele denied Holland, Zhi and Iwelumo respectively in an incredible spell of penalty-box pinball.
Albrechtsen then misjudged the bounce of the ball to let in Sam and the Charlton midfielder flashed a shot just wide of the far post from an acute angle.
Sherjill MacDonald missed a great chance to put the result beyond doubt three minutes from time when he failed to convert fellow sub Brunt's cross from six yards.
And that miss proved costly when the visitors leveled in the first minute of stoppage time.
Zhi's cross was helped on by Sam and sub Dickson rifled home his first-ever Charlton goal from close range to take the tie into extra-time.
MacDonald's frustration in front of goal continued ten minutes into the first extra period.
Bednar burst down the right and centred to the unmarked ex-Ajax ace who could only stab straight at Weaver. The loose ball squirmed towards the goalline before Madjid Bougherra cleared in the nick of time.
Brunt then exchanged a great one-two with MacDonald to burst into the box, only to see his goalbound drive deflected wide by the frame of McCarthy.
With legs getting wearier by the second, Charlton threatened in the 110th minute when Dickson beat Kiely - who had raced well out of his area - to Yassin Moutaouakil's ball before firing into the side-netting from an acute angle.
And the hosts had an ever bigger let off in the 117th minute when Dickson's low drive cannoned off the near post and hit Kiely before the Albion No.1 pounced on the loose ball.
That proved the final chance as the tie went all the way to a penalty shootout.
Varney smashed the first spot-kick off the bar but the visitors were soon level when Greening saw his effort saved by Weaver.
It was advantage Albion again when Kiely denied Zhi before Bednar rammed home the decisive tenth penalty to fire the Baggies into the fourth round for the third time in four years.
ALBION (4-4-2): Kiely; Hoefkens, Barnett, Pele, Albrechtsen; Gera (Koren 73), Morrison, Greening, Teixeira (Brunt 73); Bednar, Miller (MacDonald 84). Subs not used: Steele (gk), Hodgkiss.
CHARLTON (4-4-2): Weaver; Moutaouakil, McCarthy, Bougherra, Youga; Sam, Holland (Dickson 83), Zhi, Ambrose (Thomas 71); Varney, McLeod (Iwelumo 63). Subs not used: Randolph (gk), Semedo.
GOALS: ALBION - Bednar (14), Morrison (51). CHARLTON - Ambrose (64), Dickson (90+1).
BOOKINGS: ALBION - Gera (foul 16). CHARLTON - Moutaouakil (foul 43).
REFEREE: M Jones (Cheshire).
ATTENDANCE: 12,691.
ALBION STARMAN: James Morrison.
PENALTIES:
0-0: Varney hits bar
1-0: Brunt scores
1-1: Dickson scores
1-1: Greening saved by Weaver
1-2: Thomas scores
2-2: Koren scores
2-2: Zhi saved by Kiely
3-2: Morrison scores
3-3: Bougherra scores
4-3: Bednar scores
PIC: SPOT ON...Bednar rams home the decisive penalty
