Graham's goal, against her former club, came just eight minutes after she was substituted onto the pitch.
The 28-year-old spent eight years at the club from 2011 to 2019, which was highlighted by her subdued celebrations when she gave Spurs the lead with a powerful strike from the edge of the box in the 76th minute.
It was a match that lacked quality throughout. The first half was a story of 'close' efforts for Tottenham. Bethany England, Celin Bizet and Eveliina Summanen all came close to opening the scoring, but they lacked composure in the final third. The second half was a similar story until Graham's powerful strike.
Charlton manager Karen Hills was unable to get the better of her former club at Brisbane Road. She managed Tottenham from 2009 to 2020, helping progress the club from a part-time amateur team to one competing in the Women's Super League.
She was appointed as Charlton's manager in 2021 where they currently sit top of the Championship.
However, Charlton rarely threatened Becky Spencer in Tottenham's goal. They had just five shots in the match and only two of them were on target. Their focus returns to their promotion push in the Championship.
Story of the match
Tottenham made four changes to the team that narrowly lost 1-0 to Manchester City in the Continental Cup. Luana Bühler, Olga Ahtinen and captain England replaced Amy James-Turner, Kit Graham and Martha Thomas. Most notably, Tottenham rotated goalkeepers as Becky Spencer came in for Barbora Votikova.
Meanwhile, Charlton made five changes to the team that drew with Lewes last Sunday. The Addicks also changed their goalkeeper as Jessica Gray replaced Sian Rogers.
Summanen was denied a Tottenham opener by the crossbar in the opening two minutes. She flicked a header on from Olga Ahtinen's corner, but could not guide it below the bar.
They continued their aggressive start as England missed a golden chance to open the scoring in the 10th minute. Gray spilt Bizet's cross into the direction of the captain, yet she fired a header wide of the open goal.
Bizet then had her own opportunity to score with 21 minutes of the clock. Grace Clinton set the Norweigian up with a well-placed through-ball after a string of intricate passes, but the winger fired over the bar from a tight angle.
Despite Spurs' three chances in the first half, the opening 45 minutes lacked quality. As the rain continued to pummel on Brisbane Road, there was a sense of concern among the Spurs faithful as they watched a performance highly similar to the one against Sheffield United in the previous round.
Shuang Wang's curling shot past the post in the final minute of the first half epitomised Spurs' struggles in the final third.
Tottenham started the second half with a high intensity. Bizet squandered an opportunity to open the scoring at the back post, whilst substitute Martha Thomas had a powerful effort blocked from within the box. Yet they had to be fearful of a counter-attack from Charlton as Tegan McGowan fizzed a powerful low shot across the face of the goal.
England has struggled for Spurs since returning from a serious hip injury in December. She is yet to score in the WSL — and the captain struggled again against Charlton. Her first chance in the first half encapsulated her troubles, whilst - in the 56th minute - she fired a tame effort wide of the left post.
The striker missed another golden chance in the 65th minute, firing a powerful shot off the bar after Amanda Nilden cut the ball back into the box.
Jessica Naz continued Spurs' search for the opening goal when she came on. In the 74th minute, the substitute found space on the right flank and cut in, but her shot was deflected into Gray's hands.
However, in the 76th minute, Spurs finally took the lead through Graham. Just eight minutes after coming on, the 28-year-old fired a low-driven shot into the back of the net from 25 yards after winning the ball back effectively.
Her shot deceived Gray in goal to send the Spurs faithful into delight. Graham spent eight years at Charlton from 2011 to 2019, which she highlighted with her subdued celebrations.
Spurs managed the game effectively after taking the lead. Charlton failed to seriously threaten Spencer in goal and - despite nine minutes of added time - the Lilywhites held on to progress into the quarter-finals.
Up next, Tottenham host Aston Villa in the WSL next Sunday, whilst Charlton host Reading in the Championship as they look to continue their promotion push.
Player of the match - Molly Bartrip
In a match that lacked quality in the final third, Molly Bartrip stood out for her defensive awareness in Tottenham's defence.
She acted as a cool and calm presence alongside Bühler for the first 60 minutes and then James-Turner for the final 30 minutes.
Charlton rarely threatened Bartrip and Tottenham's defence, but it was hardly possible due to her composure in the defensive third.