Mollie crossed for Rosie to calmly slot home from close range in added time as the ladies came from 2-1 down with just 10 minutes remaining to win the FA Women's Premier League South encounter 3-2 in Somerset.
Wendy Martin scored twice and just as vital, a fantastic save from debutant goalkeeper Sarah Walters with Keynsham 2-1 up in the second half.
"The spirit we showed in the last 10 minutes was incredible," said manager, Karen Hills, as the team made it two wins and a draw in their opening three league matches.
It all started so well after the long trip to the South-West.
The ladies dominated the first 10 minutes and after a spell of pressure from the home side, went ahead five minutes before half-time when Wendy glanced home Kim Lane's free-kick.
Keynsham came out fighting in the second half. Rachel Stowell levelled on 53 minutes and Leanne Lapham steered home a cross for 2-1 just after the hour.
Goalkeeper Sarah then produced the key moment with a save from a free-kick at 2-1.
The arrival of Amy Cooper and Rosie Kmita helped Spurs chase the game down in the final 10 minutes.
On 82 minutes, Jo Woodgate fired a free-kick at goal, the ball was fumbled and Wendy was there to rifle home the loose ball.
With time running out, Wendy took a free-kick deep in the Spurs half, Jo found Mollie Kmita who beat her player and crossed for sister Rosie to convert.
Karen added: "I'm very proud with how the girls came back from what looked like being a bit of a disaster in the second half.
"When we got back on level terms I would have been happy to see the game out and take a point, but the quick thinking from the team right at the end showed how much they believed they could take all three points.
"We weren't at our best but we kept going, rode the pressure at times and then hit the two late goals. It was really encouraging."
The ladies are in cup action this weekend with a trip to Gillingham in the FA Womens Premier League Cup.
Spurs Ladies v Keynsham: Sarah Walters, Natalie Crafton, Kim Lane, Robyn Downie (Amy Cooper, 64), Jenna Schillaci, Shannon Maloney (Mollie Kmita, 79), Bianca Baptiste, Rosie Kmita, Wendy Martin, Andra Marcoci.