Ching headed home the only goal from a De Rosario corner kick in the 13th minute and Houston retained its lead through numerous Luis Angel Firpo attacks and the ejection of defender Eddie Robinson to win the final game in Group B, 1-0.
Houston is the only team carrying the MLS banner into the quarterfinals. Chivas USA and New England were eliminated in the preliminary phase and D.C. United finished bottom of Group A, but the Dynamo - playing its 48th competitive match of the year - garnered some satisfaction after elimination in the conference semifinals thwarted its attempt to win a third straight title.
Concacaf will hold a draw Dec. 10 to determine the four quarterfinal matchups. The other participants are Mexican clubs UNAM, Santos Laguna, Atlante, and Cruz Azul; USL-1 club and Caribbean surivivor Puerto Rico; Canadian representative Montreal; and Marathon of Honduras.
A rough match yielded 39 fouls, 27 of them committed by Houston. Robinson went off in the 82nd minute for a harsh kick into an opponent's calf, and Firpo substitute Carlos Calderon followed him in stoppage time by drawing cautions just four minutes apart.
Needing a win to advance, Houston forced Firpo back from the opening kickoff and generated four corners in the first 13 minutes. On number four nobody picked up the mark on Ching, and from just outside the goal area he powered DeRosario's right-footed inswinger off the right hand of goalie Juan Jose Gomez and just under the crossbar.
Houston's dominance ebbed as the first half waned and it needed keeper Pat Onstad to save smartly from Patricio Gomez in the 37th minute before nearly doubling the lead before halftime. Corey Ashe, the main danger man in the first half, and De Rosario got good looks but neither could convert.
The Dynamo's lack of fitness and sharpness - it hadn't played a competitive match since Nov. 9 - enabled Firpo, strengthened by the arrival of halftime sub Francisco Medrano, to test Onstad a few more times, and on each occasion the 40-year-old Canadian, dubbed "Big Pat" by Coach Dominic Kinnear, played up to his name.
In the 54th minute, he stopped Fernando Leguizamon, and two minutes later, against the same opponent, Onstad dived left to stop a bouncing shot. Kinnear removed Jaqua for Kei Kamara, whose zip and energy defused Firpo's rhythm, and also brought on Richard Mulrooney. Robinson's ejection prompted the arrival of defender Pat Ianni, and Houston withstood a few set plays - and a brief goalmouth cameo by goalkeeper Gomez - to land a spot in the last eight.