The 18-year-old, who has been linked with a move to the Premier League champions, had been on the pitch for barely a minute when he stroked home Everton's third goal in the closing seconds.
Dimitar Berbatov opened the scoring for United but goals by Diniyar Bilyaletdinov and substitutes Dan Gosling and Rodwell gave them the points.
Everton were appealing for a penalty as early as the 14th minute when ex-Toffee Wayne Rooney appeared to shove John Heitinga in the back.
But referee Howard Webb waved play on and the reigning champions made the most of their break in clinical fashion less than two minutes later.
Antonio Valencia's threaded cross made its way to Berbatov and the Bulgarian took one touch before hammering home the opener from ten yards.
But Everton were only behind for three minutes when Bilyaletdinov rifled home a stunning effort from outside the box which left United keeper Edwin van der Sar rooted to the spot.
The hosts then had more cause to complain when Wes Brown handled Leighton Baines' cross in the box but again their protests were again waved away.
Everton started the second half the stronger but nearly found themselves a goal down when Rooney teed up Darren Fletcher who rifled wide of the mark. Rooney then crossed for Berbatov to head wide of the mark as United started to turn the screw.
But Everton boss David Moyes shuffled his pack and the introduction of Gosling for goalscorer Bilyaletdinov breathed new life into the Toffees.
And it paid immediate dividends as, after less than five minutes on the pitch, Steven Pienaar's pull-back found the young midfielder who turned the ball home.
With 15 minutes remaining, United predictably through men forward but it left them exposed at the back and Rodwell capitalised in the dying stages with a brilliant run and finish.