Both teams had scored wins over Wales and Malaysia, and lost to Australia, making their clash at the National Hockey Centre on Glasgow Green a straight face-off for a place in the last four.
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Danson and Townsend struck inside the first half-hour, with Nikki Kidd slotting a consolation strike for the Scots.
Danson made a 15th-minute breakthrough when she took on a pass from Nicola White and fired past busy Scotland goalkeeper Amy Gibson, and Townsend doubled the lead after 27 minutes from a penalty corner.
A Scottish reply from Kidd followed four minutes later, after another penalty corner, but the home side could not find an equaliser despite putting intense pressure on England.
Goalkeeper Maddie Hinch kept England ahead, and Danson said of the success: "We are obviously delighted with the win. The game was exactly what we thought it was going to be it, it was tight and Scotland had obviously done their homework.
"They won lots of corners but we are delighted, we stuck to our task and are over the moon to be building momentum for the next game.
"We are so delighted to be in the semi-finals, it's been a big competition from day one because we had a lot to prove to ourselves.
"But for us it is all about building momentum and every time we have done that."
Head coach Danny Kerry added: "The first half was very good, Scotland over-exposed themselves and we exploited that.
"In the second half Scotland stepped up and that generated some anxiety but in the last 10 minutes we got some good experienced players on the pitch and that allowed us to see it out."