Stewart, who finished unbeaten with 87, received the Man of the Match award for his part in a decisive second wicket stand of 174.
Having ended last summer's triangular series with scores of 74 not out, 101, 100 not out and 97 against Zimbabwe and the West Indies, he has now scored five consecutive one-day half-centuries.
But Hussain's contribution here was even more encouraging for England.
"I wanted a hundred but you will always take 95, no matter who it is made against," he said. "I was a bit nervous at the start, but I was pleased with the way I played and pleased with the all-round performance of the team."
Hussain entered the fray once Marcus Trescothick had edged a catch behind with the total 33. The skipper was stuck on nought for 11 deliveries and twice beaten outside off-stump by paceman Mushfiqur Rahman. But then the same bowler finally offered some width, Hussain drove him square and all the anxiety of the last few months seemed to fall from his shoulders.
What followed was a joy for English eyes as the captain stroked five sixes and another eight fours.
By then, England were virtually home and dry. Stewart cruised through to the finishing line, Graeme Hick clubbed 23 quick runs and it was all over well inside the allotted distance.
England's next task will be considerably more difficult with South Africa waiting to do battle with them in Tuesday's quarter-final. But Hussain and Co are off and running at the start of this long and difficult winter campaign.
