Stalwart Ryan Giggs gave United a 35th minute lead with a sweetly-struck shot but Chelsea's new France winger Florent Malouda levelled with a fine solo goal on the stroke of halftime.
Neither side created a clear-cut chance after the break, leaving the traditional curtain-raiser for the English top-flight to be settled by a shootout in front of a crowd of more than 80,000 at Wembley.
Wayen Rooney struck the winning penalty to give his side first blood in what is expected to be another season-long battle between the two clubs for domestic honours.