Victory at Villa Park, where Chelsea's Frank Lampard shot over the crossbar from close range in the 90th minute, would have seen the Blues reduce United's lead at the top to four points.
The point was Villa's first in five games, Martin O'Neill's team becoming the first side in the Premiership this season to stop Chelsea from scoring.
Henry, the Arsenal captain, had been out of action since November 29 - a run of seven league games - because of a problem with his sciatic nerve.
But the France striker was soon back into the old routine.
He scored from the penalty spot in the 30th minute after Charlton full-back Osei Sankofa was sent-off for pulling back Robin van Persie in front of an open goal.
Full-back Justin Hoyte added a second goal for the home side in first-half stoppage time before van Persie put the result beyond doubt with two goals, the first from the penalty spot, inside the final 15 minutes.
The north London club's victory meant that English football's "big four" of United, Chelsea, Liverpool and Arsenal occupy all four Champions League qualifying places.