Just six days after scoring both goals in the Ryman Cup Final that Charlton took in extra time at Ware FC, Graham repeated the trick to sink Spurs in the final minute of Wednesday night's FAWPL South clash at Thamesmead.
Once again, Spurs matched a title-chasing team but as manager Karen Hills pointed out, once again it was 'the finer details' that cost her team.
Both teams had chances in the first half - Wendy Martin lobbed Spurs' best chance just wide before Charlton capitalised on a mistake for Graham to open the scoring two minutes before the break.
Charlton had chances at the start of the second half and struck the woodwork but Spurs clawed their way back into it and finally levelled just four minutes from time when Baptiste headed home from a corner.
However, Graham once again had the final word as she broke through with Gemma Shepherd, exchanged passes and finished low with 90 minutes on the clock.
"That was a tough defeat for the girls to take," said manager Karen. "We certainly had the chances and finally got ourselves back into the game only to lose it right at the end.
"We gifted the first goal to them at the end of the first half and as I said, we had the chances, but it's the finer details that are making all the difference.
"The players have given everything in three high-profile games in a week, including the cup final and we've played as well as we've played for a long, long time but we've ended up with nothing.
"I can't knock the girls. They have given everything this week, their commitment is fantastic and we're going places.
"We've got a free weekend now and they deserve a break. We'll get back into training next week and then we've another big game against Cardiff."
Spurs Ladies have three matches remaining in the FAWPL - Cardiff at Ware FC on Sunday, May 3, Copsewood Coventry away on May 10 and finally QPR (date TBC).
Spurs Ladies v Charlton: Toni-Anne Wayne; Rosie Kmita, Sophie McLean, Jenna Schillaci, Lucia Leon; Wendy Martin, Shannon Maloney, Riana Soobadoo; Bianca Baptiste, Katie O'Leary, Avilla Bergin. Subs: Leah Rawle, Eartha Pond, Andra Marcoci, Lauren Picton.
SPURS LADIES MICROSITE