Tottenham once again proved to be a difficult opponent after Evaliina Summanen cancelled out Sam Kerr's first-half goal with a superb free-kick.
Yet Chelsea, on the back of an intense run of fixtures, still managed to advance to the semi-finals when substitute Buurman hit a wonderful left-footed effort from the edge of the penalty area four minutes from time.
The Chelsea head coach was proud of her players and explained they were suffering from fatigue coming into this final encounter before the international break.
'Mentally, we were strong and confident,' said Bompastor. 'Even when we had that moment where we conceded the goal, we suffered a little bit, but we stayed confident, and I think we played with confidence.
'We knew we'd have enough quality to still create in the game and be able to score. So that's big proof of our experience, I think. Most of the game, we were in control.
'We came into this game with a lot of fatigue and heavy legs. We didn't have a lot of players to rotate in the seven games we played in the past four weeks. So I think that's completely normal for the players to feel like that physically.
'But mentally, I'm really proud of them. They put in the effort and they were fighting until the end. The quality was shown on the pitch again.'
Defender Buurman has made 17 starts for Chelsea since making her debut at the beginning of this season and has proven her worth on the biggest of stages.
Today's match saw her introduced on the hour mark after playing intensive minutes since our Women's League Cup final win in mid-March, and she took the opportunity to make her mark by scoring the game-winner with no time remaining for Spurs to reply.
'I think, when you analyse everything, it's amazing,' Bompastor said of the Dutch international. 'She is young. I think for her, this last block was a big achievement. She had great performances out of possession, but also with the ball, and today she had a great performance again, and her goal was a rocket.
'So I think for her to be able to score that type of goal, it's really nice. She helped the team perform, but she’s also helped win a really important game. So for a teenager like her to be able to have this impact in a team like Chelsea, it means a lot.'