Chelsea's hopes of winning a third consecutive Premier League title have taken a knock with a third straight draw, their first match this season without scoring.
United, who drew 2-2 at Newcastle United on Monday, are top of the table with 54 points from 22 games, Chelsea have 48 and Liverpool are a distant third on 40 points.
Arsenal moved up to fourth on 39 after Henry scored a 30th minute penalty following a red card for Charlton defender Osei Sankofa and then set up defender Justin Hoyte to score his first for the club.
Robin van Persie converted another penalty in the 76th minute and the Dutch forward added their fourth at the very end.
The day's spotlight was on Villa Park, where the champions had been hoping to shake off consecutive 2-2 draws against Reading and Fulham.
Chelsea dominated the first-half possession but their best chance was squandered by Ivory Coast striker Didier Drogba, whose downward volley bounced over the crossbar.
Drogba continued to be a menace after the break and England midfielder Frank Lampard shot on sight as Jose Mourinho's men laid siege to the Villa goal in the closing stages.
A resilient Villa side were better than in the opening 45 minutes and might even have snatched a win with a Liam Ridgewell header that flew wide, but Lampard missed a great chance at the end as he blasted over the bar.
CHELSEA ALIVE
Asked about the gap on United, Mourinho told Sky Sports: "Six points...is not bad and the way the team fought and the way they have behaved in the difficult moments we are living I have a lot of hope for the second part of the season."
"We are alive...we believe in us."
Lampard bitterly regretted his miss, saying: "I'm gutted for the lads because we came here, worked hard and I should have stuck that away."
Arsenal, beaten by Sheffield United on Saturday, were clearly lifted by the return of the talismanic Henry, who last played in their defeat by Fulham on November 29.
He hit the post with an early header before sending goalkeeper Scott Carson the wrong way with his spot-kick.
The France striker followed up by providing the pass in a one-two with goalscorer Hoyte just before the break and won the penalty converted by Van Persie after a foul by Souleymane Diawara.
Asked about his captain's return, manager Arsene Wenger told Sky Sports: "Of course, it was a boost, individually and psychologically for the team."
Henry played it down, though, saying: "What was important was getting the three points after the disappointment against Sheffield United."
