"We've had one good day, one great day - but there's still four days of hard work left."
England won the toss at the Melbourne Cricket Ground and captain Andrew Strauss decided to field.
The Australians were then dismissed for their lowest total against England at the MCG and their lowest against the visiting side at any ground since 1968.
"Throughout the series, we've bowled really well - beat the bat a lot - we've had lbws turned down and created chances," added the Lancastrian.
"Today was the day when all those bits of luck came together, and we got the nicks."
The Ashes series is currently tied at 1-1 after Australia recorded an emphatic victory in the previous Test at Perth.
"We've been good at bouncing back strongly, so we didn't expect anything less - but to do it so emphatically probably wasn't on the cards," added Anderson.
"It's an amazing feeling."
After the crushing defeat at the Waca, when England found the extra bounce difficult to combat, the drop-in pitch at the MCG where the turf is pre-prepared and lifted into place, proved much more to their liking.
"When we bowled them out it was very similar to English conditions, not a great deal of pace in the pitch but a little bit of sideways movement which is always nice and the overcast conditions helping the swing as well," Anderson said.
"We didn't over-attack, all the catches seemed to be going to first and second slip and the keeper so the need for a third slip wasn't there, we put him at extra cover and it worked brilliantly for us."
One of Anderson's victims was the obdurate left-hander Mike Hussey, who had scored 517 runs in five previous innings in the series, with a lowest score of 52.
Hussey made only eight from 41 balls before Anderson had him caught behind by Matt Prior.
"I was just trying to hit the seam trying to wobble the team and let it move both ways and hit an area that if it did move it would ask questions inside and outside the bat and luckily that one went away from him," the 28-year-old Lancastrian explained.
"It was something we talked about whether we had the right plan for him or not and we decided we did have the right plan, we just needed to stay patient with him and it paid off.
"We had the extra cover in to encourage us to pitch it up so with the extra movement we were getting I felt comfortable to pitch it fuller and slightly straighter and it did work."
England then finished with an unbroken partnership of 157 between Strauss and fellow opener Cook, to give the visiting team a lead of 59.
"We were delighted to do that but we were a bit unsure what the wicket was going to do when they bowled," he said.
"Our two guys batting did fantastically well but we're going to have to bat well, bat once, then bowl particularly well on the last couple of days."
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