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The home side's advantage lasted until just before the half-hour mark. Grant Leadbitter whipped an inviting cross into the box and Jonathan Woodgate found the net with a diving header.
Hulse could have restored Charlton's lead shortly before the half-time whistle, but he missed the target with a free header.
Charlton almost hit back through Wright-Phillips on the hour mark, but Boro extended their lead moments later through a superb Emmanuel Ledesma effort.
The Argentine caught Ben Hamer off his line and lobbed him with a pinpoint chip from just outside the area to put the game beyond their opponents.
Boro added a fourth late on through substitute Richard Smallwood to cap off an impressive win that puts them joint-top of the Championship.