James Anderson did the damage with the new ball taking early three wickets and with Jade Dernbach, Tim Bresnan and Stuart Broad consistently hitting the right areas on a green looking pitch the tourists were bowled out for 175.
A brief shower meant England’s target was reduced to 171 and they got there in double quick time. Cook smashed 95 from 75 balls and opening partner Craig Kieswetter chipped in with a boundary-laden 72.
After suffering equally comprehensive defeats of their own at Lord’s and Headingley, England, and their captain in particular, were delighted with the response.
Cook said: “I don’t always time the ball as well as that, a couple of innings don’t stop criticism and I have to do that over a period of time.
“It was outstanding, we were lucky to win the toss; the way we bowled was fantastic and put them under pressure and then knocking them off without losing a wicket was great.”
Cook’s batting decorated the victory but it was Anderson’s skill up front that put England in a position from which they were unlikely to do anything but record a convincing win.
Cook added: “Jimmy was outstanding. They all bowled well, I was really pleased for Stuart Broad to pick up some wickets and Jade Dernbach bowled well in the power play.”