The duo won the first set in the World Tour quarter-finals in Cape Town, South Africa, but in the second set the world No. 2s caught up.
1-1 in sets paved the way for a third and deciding set - which turned out to be a thriller.
But Åhman/Hellvig turned the deficit of 11–13 into a 23–23 victory and are thus through to the semi-finals.
"We play extremely well in 1.5 sets and we were on our way to a 2-0 victory.
Then we lose everything and get overrun the rest of the second set.
In the decisive set, we are once again very good in attack, but we have great difficulty in stopping the Dutch", writes coach Rasmus Jonsson in a text message to SVT Sport.
He points out that patience and coolness were the keys to winning the last set.
Currently, the Swedish duo is ranked 12th in the world.
Next, they face Qatar's Cherif/Ahmed, ranked sixth in the world, in the semi-finals.