Latching onto a loose ball just outside the box, the Frankfurt playmaker launched a right-footed strike and across Sweden goalkeeper Hedvig Lindahl and into the bottom left corner on 99 minutes.
"I just saw a good angle. We've talked about it for a couple of weeks that I need to take shots more often. The ball just came really nicely and I thought, 'let's do this,'" Groenen said after the game.
With their extra-time victory, Sarina Wiegman's team set up a final showdown with defending champions the United States here in Lyon on Sunday. Sweden will play England in the third-place playoff match in Nice on Saturday.
"It's the whole development in the Netherlands and also the individuals that made bigger steps," said Wiegman. "They are very experienced now, and they believe they can perform well."
"Belief is also one of the things that made it happen," she added.
Sweden coach Peter Gerhardsson was magnanimous in defeat. "We're playing a very skilled team. That's what happened," he said at a post-match press conference.
"Now it's about the medal. Ending up third of course feels a lot better than ending up fourth. We'll do everything in our power to try to do that," he added.
This was the first ever Women's World Cup semifinal to go to extra time, as the Dutch women, appearing in their first semifinal of the quadrennial event, started sluggishly but managed to hold Sweden 0-0 after 90 minutes.
The Oranjeleeuwinnen had only one shot on target to their name in the first half, while Sweden looked lively in possession, especially down the right wing.
Elin Rubensson, who started in place of Nathalie Bjorn after the latter was laid low with illness, had a shot blocked on 37 minutes before Lina Hurtig's follow-up was hacked away by Sari van Veenendaal.
The 2003 World Cup runners up started the second half strongly, as Nilla Fischer's low strike from inside the box hit the post in the 56th minute before Desiree van Lunteren cleared the ball.
And whatever Wiegman told her players in the dressing room, it obviously worked, with more attacking impetus from the Dutch in the second half.
Vivianne Miedema created the best chance for the Netherlands in regular time as the Arsenal forward made a looping header from a corner kick on 64 minutes, but Swedish keeper Lindahl tipped it onto the crossbar.