Danson netted in the opening exchanges, only for her strike to be cancelled out by a Macarena Ronsisvalli penalty corner minutes later.
The Reading striker scored again to restore the hosts advantage and Hannah Macleod, making her 50th England appearance, put more distance between the sides just seconds later.
But Italy, ranked 17th in the world, belied that position with a strong second half showing and Agustina Di Bernardo's 56th minute goal gave England coach Jason Lee some anxious moments.
The win all-but guarantees England a place at the 2014 World Cup as, while the top three sides from this tournament qualify for the finals, the likes of Argentina and South Africa are expected to 'double qualify' through their continental competitions.
"We’re quite a new group and we expected the competition to be tough," Lee said.
"We started to run out of legs a bit, the nerves started to kick in and our inexperience started to show. I think Italy are playing above 17 in the FIH world rankings and no doubt they’ll be pushing hard on the European stage soon.
"They broke down tackle after tackle, finding their way into our circle which certainly made it nerve wracking. It was quite a tense game for everyone and we’re very pleased with the outcome.
"Once again the girls fought so hard for the win and I think that’s what has ultimately helped us get here.”
But captain Kate Walsh knows her team will need to improve when they take on world number two side Argentina on Saturday.
“For Argentina we should go in with no fear," she said.
"We need to approach the game not thinking of individual players but of our own play, and we need to show that fearlessness of youth which I think we have in our squad - we’re really looking forward to this match.”