Neither side created a clear-cut chance after the break, leaving the traditional curtain-raiser to be settled by a shootout in front of a crowd of more than 80,000.
The penalty from Rooney, whose team had lost that FA Cup final in May, gave United first blood in what is set to be another long battle between the two clubs for honours.
United manager Alex Ferguson told a news conference: "We've always used it as a stepping stone towards the first game of the season and I'm pleased with it.
"I don't think there was much between either side, particularly in terms of possession, but we did make the clear chances and for that reason we probably deserved to win."
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