After Wilman Conde's equalizer for Chicago in the 81st minute, the Hawaiian-born forward secured the win for Houston when he headed a corner kick by Richard Mulrooney just inside the right post four minutes later.
Lovel Palmer scored his second goal of the season and Mulrooney was involved in all four goals for the Dynamo, whose last win was 2-0 over D.C. United on May 22.
Ching recorded his first hat trick since the franchise's first game in April 2006 and now has six MLS goals in 2010.
Ching used a left-footed shot to give the Dynamo a 1-0 lead in the 31st minute after Fire goalkeeper Sean Johnson dropped a corner kick by Mulrooney. That gave the Dynamo its first lead since July 1 at Toronto.
Palmer extended Houston's lead to 2-0 in the 50th minute, when the Dynamo scored on yet another set piece. But the Fire made it 2-1 when Calen Carr powered a shot by Pat Onstad in the 55th minute.
Ching scored a pretty bicycle-kick goal four minutes later to give Houston a 3-1 lead. Bobby Boswell hit the crossbar, but the rebound ended up just outside the goalkeeper box. With his back toward the net, Ching jumped and scored his second goal of the night in the 59th minute.
The Fire got within a goal in the 59th minute when Boswell rolled an own goal by Onstad to make it 3-2.