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Arsenal already led through Henry's spectacular 13th-minute effort. He broke from inside his own half, nipped past two challenges and curled a left-foot shot past keeper Kasey Keller.
Tottenham rarely tested David Seaman's Premiership debut-making deputy Rami Shaaban. He made his most difficult save in the third minute, from Jamie Redknapp's shot.
Dean Richards wasted Spurs' best second-half chance with a weak finish.
Wiltord and Henry had goals disallowed for tight offsides as Arsenal threatened to run riot. The champions wrapped up the points in the 55th minute. Henry dummied a defender and crossed for Ljungberg to score from six yards after a trademark run into the box.
Robert Pires lobbed Keller only for the ball to drop on top of the net and Wiltord bent a shot inches wide, before Arsenal netted their third after 71 minutes.
Pires played Henry through. Keller blocked his point-blank shot and Pires slipped the rebound across for Wiltord to turn the ball in.
Tottenham will view Davies' dismissal as a turning point, but this was their fifth game without a win and they are sliding after a bright start.