Addicks skipper Johnnie Jackson came to the away side's rescue in the first half when he cleared a header from Neill Collins off the line. United's Ched Evans then saw his shot deflected wide shortly afterwards.
Michael Morrison had Charlton's best chance before the break but he drove wide from a great position.
The visitors did break the deadlock, however, in the 65th minute through substitute Kermorgant, who met Jackson's corner with a firm header just moments after coming on.
And Wright-Phillips increased Charlton's lead just two minutes later. The striker found himself through on goal after a defensive lapse and, after the ball rebounded into his path following Steve Simonsen's block, Wright-Phillips turned home into the empty net.
Danny Wilson's side rarely threatened to mount a comeback. Michael Doyle sent a long-range effort just wide and Evans thumped the woodwork with a shot at the death.