Captain Casey Stoney scored a third late in the match.
The result sees England leapfrog the Netherlands to qualify from their group in top spot, although the Dutch also reach the finals in Sweden as best runners-up.
"It is a relief to qualify automatically as it means we don't have to go through the danger of the play-offs," said coach Powell. "Now we can focus on next year. In patches, I thought we played very, very well."
Pre-match build-up at Walsall's Banks's Stadium had focused on how many England would score, not whether they would win.
But Powell's side found the Group Six basement side less obliging than they had on their visit to Croatia.
England were at fault for poor passing and even poorer crossing in the first quarter of the match, although tight marking from their opponents made life difficult.
The home side got most joy down the flanks, with Steph Houghton, impressive for Team GB at the Olympics, a key figure in the moments leading up to the first goal.
The Arsenal full-back sped down the left wing before delivering a low ball into the centre. An alert Aluko struck a first-time low shot that keeper Doris Bacic failed to hold, allowing Scott to tap in.
Two minutes into the second half, England extended their advantage.
Euro qualification pleases Powell
This time the assist came from Rachel Yankey, on her record 120th England appearance, who played a low cross into the area. The Croatia defence failed to clear the box and Aluko improvised quickly to poke the loose ball in off the post.
Teenager Bacic twice denied Birmingham's Karen Carney, arguably England's player of the match, and blocked Fara Williams's effort, but could do nothing to stop captain Stoney scoring the goal of the game.
It was again Carney who did the initial damage, leaving her marker for dead on the left and firing in a low ball that Stoney swept into the net.
Bardsley, Alex Scott, Bradley, Stoney (Rafferty 87), Houghton, Jill Scott, Asante, Fara Williams, Yankey (Duggan 79), Aluko,Carney.
Subs Not Used: Brown, Clarke, Susi, Bassett, Rachel Williams.
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