United, preparing for their Premier League title defence without the departed Cristiano Ronaldo and Carlos Tevez, took an early lead through the impressive Nani.
Carlo Ancelotti's side improved markedly after the break and Ricardo Carvalho headed them level seven minutes after the interval before Frank Lampard struck with 20 minutes to go.
Wayne Rooney, who was joined in attack for the final 15 minutes by United's new signing Michael Owen, then showed a cool head to beat Chelsea keeper Petr Cech in stoppage time after being sent clear by Ryan Giggs.
It proved in vain for United, however, as Giggs and Patrice Evra both had their spot kicks saved by Cech and Salomon Kalou fired high past Ben Foster to settle it, with Chelsea winning the shootout 4-1.
(Reporting by Martyn Herman; Editing by Sonia Oxley)