Kennedy tugged at Steve MacLean's arm as he darted into the box, and referee Simon Hooper pointed to the spot and brandished the red card to Kennedy, who had been the last man.
MacLean then converted the 64th-minute penalty, although keeper Andy Warrington half-stopped it, only to see the ball spin over the goalline.
Oxford took the lead in the 18th minute with a precise right-footed shot by Simon Heslop from 15 yards, from Jack Midson's cutback.
However, the Millers equalised 18 minutes later when Nicky Law nipped in ahead of U's keeper Ryan Clarke to turn in Kennedy's pass with an angled shot.
James Constable squandered two opportunities to extend Oxford's lead before the finish, and sub Alfie Potter curled a shot wide as Chris Wilder's men continued to push forward.
It was their first win in four games and avenged a 2-1 defeat at Don Valley Stadium in November.
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Source: DSG