Charlton twice came from two goals behind to deny Town all three points at The Valley.
Goals from George Edmundson and Tyreece John-Jules had put the Blues ahead in the capital before efforts from Jes Rak-Sakyi and Albie Morgan saw the hosts level the game.
Freddie Ladapo and Sam Morsy fired the Blues back into a two-goal lead in stoppage-time but Terell Thomas and George Dobson struck late on to snatch a point for the hosts.
Ed Sheeran was also in attendance at The Valley this afternoon.
Morsy returned to the starting XI in one of three changes from the midweek victory over Port Vale. John-Jules and Kayden Jackson also came back into the side with the trio they replaced - Cameron Humphreys, Kyle Edwards and Freddie Ladapo - named amongst the substitutes.
The first chance of note did not come until midway through the first half. Davis played a slick one-two with John-Jules down the left side before pulling the ball back to the middle of the box for the arriving Conor Chaplin. Town's number 10 struck his first-time shot well but saw it blocked by a couple of Charlton defenders.
Six minutes before the interval, Morsy cut the home defence open with a through ball to John-Jules. For a second time, a whistle was blown in the home end in an attempt to disrupt a Town attack before the Arsenal loanee saw his shot deflected behind by Eoghan O'Connell. The defender picked up an injury in the process of making a block that likely denied the opener and became the second home player to go off injured inside the first half following Mandela Egbo's premature exit from the pitch.
John-Jules had an even better opportunity early in additional time but, after taking in a Davis pass and turning his man inside the box, his shot was blocked on the line.
From the resulting corner, the Blues moved into a deserved lead as Davis' in-swinging delivery was met by a powerful Edmundson header which Charlton 'keeper Joe Wollacott could only palm into the roof of the net.
Town made it 2-0 early in the second half through another headed effort. This time, John-Jules timed his run perfectly to nod a teasing Wes Burns cross into the back of the net from close range to send the travelling 3,139 fans at that end into pandemonium.
Charlton manager Ben Garner was first booked then sent off for his persistent appeals from the sidelines following the second goal.
The hosts found a response on 63 minutes. Christian Walton pulled off a stunning reaction save to deny Corey Blackett-Taylor's volley following a deep cross but the loose ball was prodded into the back of the net by Rak-Sakyi.
John-Jules was denied from close range at the other end just a minute later as his header following Davis' cross from the left was turned away by the feet of Wollacott.
Charlton equalised with just under 15 minutes remaining. Blackett-Taylor cut in from the left wing and saw his lot shot saved by Walton but Morgan hammered in the rebound.
Kyle Edwards had a great opportunity to regain the advantage five minutes from time after a low pass from Davis had fallen into his path however the winger sliced his shot wide of the mark from the middle of the box.
Ladapo and Morsy fired in powerful low efforts from 20 yards in stoppage-time to seemingly win the game for the Blues.
Thomas and Dobson netted late on to snatch a point for Charlton.
Town: Walton, Donacien, Woolfenden, Edmundson, Burns (Keogh 90'), Ball, Morsy (C), Davis, Chaplin (Harness 71') , John-Jules (Ladapo 71'), Jackson (Edwards 71').
Subs: Hladky, Vincent-Young, Humphreys.
Booked: Ball, John-Jules, Morsy, Burns.
Charlton: Wollacott, Clare, Thomas, O'Connell (Lavelle 43'), Egbo (Morgan 14'), Dobson, Fraser, Kirk (Blackett-Taylor 62'), Rak-Sakyi, Stockley (C) (Aneke 62').
Subs: Macgillivray, McGrandles, Payne.
Booked: O'Connell, Dobson, Clare, Garner (manager).
Sent off: Garner (manager).
Attendance: 16,625 (3,139 Town fans).
