After a superb defensive show, the National League South underdogs finally conceded in the 71st minute and eventually lost 4-0.
But that was only after Hawks defender Sam Magri had been stretchered off just after the hour mark and Charlton keeper Stephen Henderson had made a great save to keep out a Jake McCarthy header shortly after when the score was still 0-0.
Josh Davison’s header broke the deadlock and Charlton - 65 places higher in the pyramid - added further goals through captain Jayden Stockley (2, 1 penalty) and sub Mason Burstow.
Hawks reserve goalkeeper Charlie Searle played the last 10 minutes up front after Leon Chambers-Parillon had limped off injured with boss Paul Doswell having used his only three outfield subs.
Doswell made three changes from the side that had won 3-2 in the National League South at Chelmsford.
In came loanee midfielder Chambers-Parillon and defenders Josh Passley and Michael Green for Scott Rendell, Abdulai Baggie and Paul Rooney. Though he was allowed to name nine subs, Doswell could only name four, including Searle, due to suspensions to Tommy Wright and Billy Clifford and injuries to Ross Worner and Alex Wall.
Hawks lined up in a 4-5-1 formation with Magri at right back and Green at left-back with Passley and Joe Newton providing midfield width and extra defensive strength.
Charlton boss Jackson made nine changes, with only Norwich loanee defender Akin Famewo and striker Stockley keeping their places in a 3-5-2 formation.
Keeper Stepen Henderson, Harry Arter, Charlie Kirk, Albie Morgan, Papa Souare and Ayodeji Elewere made their first appearances since Nigel Adkins was sacked last month.
Henderson’s first competitive appearance since appearing for Wycombe almost three years ago, in December 2018.
Ex-Pompey pair Craig MacGillivray and Jason Pearce were among the nine Addicks subs, of which five could be used.
The Addicks, to no-one’s surprise, dominated possession in the first half but Hawks turned in a very organised defensive display in a first half of few clear chances.
Charlie Kirk and Harry Arter tried their luck from distance early on, but neither shot was on target as the hosts attacked the Jimmy Seed Stand holding the noisy travelling fans.
Albie Morgan, born in Portsmouth, cut inside on 20 minutes but dragged his effort wide.
It took Hawks 27 minutes to create any alarm in the Addicks defence. Passley found himself in space on the right and his floated cross went over Henderson’s head but drifted just wide of the far post.
With James Roberts operating as the lone Hawks striker, the home defenders had ample time to pass the ball among themselves and build attacks that way.
Sean Clare, one of three central defenders, and Kirk both managed to get in on-target shots, but neither was a problem for Mannion.
On 39 minutes Hawks got their first set-piece in a decent position, but Passley’s inswinging free-kick from the left side was easily gathered by Henderson.
Just before the break, Passley was given another chance from a free-kick on the right side - but this time Henderson was able to punch clear.
In between, Elewere strode forward from the back to fire a 25-yarder well over Mannion’s bar.
Overall, though, Doswell would have been very satisfied with his side’s first 45-minute performance.
Hawks managed their first on-target effort on 48 minutes when Chambers-Parillon shooting straight at Henderson.
Magri went down injured on 57 minutes and, after lengthy treatment, was stretchered off with Paul Rooney coming on to replace him.
Hawks forced their first corner of the tie on 67 minutes and it saw McCarthy get in a close range header which Henderson clawed away diving to his left.
Charlton made a double change on 70 minutes,bringing on Elliott Lee and Ben Watson, the latter an FA Cup final goal hero with Wigan in 2013.
Sixty seconds later Charlton took the lead when Kirk stood up a cross from the left-hand side of the Hawks penalty area and the unmarked Davison could hardly miss with a back post header.
It was 2-0 on 75 minutes when Lee was tripped by Jamie Collins and Stockley confidently converted the penalty.
Stockley grabbed his second from close range 10 minutes later after Lee’s effort had struck the underside of the bar. And teenage sub Mason Burstow drilled home Charlton’s fourth just before six minutes of stoppage time started.
Charlton: Henderson, Elewere, Famewo, Souare (Clayden, 86), Morgan (Lee 70), Kirk, Arter (Watson 70), Blackett-Taylor, Clare, Stockley (Burstow, 86), Davison (Washington, 90+2).
Hawks: Mannion, Passley, Newton (Rendell, 76), Oastler, Magri (Rooney, 62), Collins (Baggie, 76), Green, Gobern, Chambers-Parillon (Searle, 83), McCarthy, Roberts.