Wicketkeeper-batsman Jos Buttler top scored with 61 yesterday as the tourists reached 264-8, before Ravi Bopara took four wickets for the loss of just three runs as England sealed a 172-run triumph.
“It’s great to win,” said Cook, who has overseen a 5-0 Ashes whitewash followed by defeat in the first one-day match against Australia.
“It’s been a long time coming. It’s very important because we need to start winning. We have a huge amount of work to do, but it’s a step in the right direction.”
Cook could engineer no such improvement in his own fortunes, falling for one to veteran bowler Brett Lee. The off-form opener has now failed to make double figures in seven of his last 10 innings.
It was left to Michael Carberry (47) and Gary Ballance (56) to build a platform, before an 80-run stand between Buttler and Tim Bresnan (36) helped carry England from 149-6 to 264-8.
Towering paceman Boyd Rankin claimed two wickets before Bopara tore through the tail end. England’s second one-day international is on Friday.