Spain made holders USA work had for a 2-1 victory with both their goals from the spot and another tight last sixteen tie saw Sweden edge Canada 1-0.
Las Rojas denied the USA a goal from open play but two Megan Rapinoe penalties put her side through for a massive clash with France,
Spain began in a lively fashion and had an early shot bravely blocked but they were behind following a fifth minute penalty which Rapinoe buried into the bottom corner.
Any assumptions of another big USA score were soon dismissed as poor defending presented Jennifer Hermoso with a chance which she took beautifully.
The game was decided by a penalty 12 minutes from time, give for a foul on Rose Lavelle and again convincingly converted by Rapinoe.
A Stina Blackstenius goal set Sweden up for a quarter-final against Germany but the Swedes later suffered some penalty scares.
Kosovare Asllani’s well-timed pass in the 55th minute gave Blackstenius the chance to clip the ball over the onrushing Stephanie Labbe for the only goal.
Canada were awarded a spot-kick when Desiree Scott’s strike was handled but Janine Beckie’s effort brought an excellent save from Hedvig Lindahl.
Sweden had their own penalty decision dismissed due to offside and even after the final whistle had to wait on discussions over a possible spot-kick against them.