Former Arsenal striker Henry got the ball rolling, before Luke Rodgers made it two five minutes before half-time.
Further goals from Joel Lindpere and Juan Agudelo (two) completed the rout.
Kansas City are now nine games unbeaten after their 1-1 draw with Colorado.
Conor Casey gave the rapids the lead in the first half, only for Graham Zusi to level after the break.
Jeff Cunningham`s dramatic 90th-minute goal helped Colorado come away from Vancouver with a 1-0 win, with Shea Salinas sent off for the home side.
In the day`s other game, goals from substitute Ben Zemanski and Nick LaBroca saw Chivas beat San Jose 2-0.