Brown's field goal was set up by a Marcus Coleman interception on a poor sideline throw by Jay Fiedler.
For the exclamation point on a poor performance by the Dolphins, Fiedler's last-second Hail Mary was picked off by Coleman at the 5-yard line.
The Dolphins were sloppy from start to finish. Their run defense was porous; Ricky Williams found little running room for most of the afternoon; and the Dolphins committed way too many penalties, including a costly (albeit highly questionable) holding penalty on tight end Randy McMichael that may have been the turning point of the game.
The Dolphins' vaunted defense also failed to come up with either a sack or a turnover.
The one player who had a big game for Miami was wide receiver Chris Chambers, who caught two touchdown passes, including a spectacular one-handed grab at the back of the end zone.
Chambers' two first-half touchdowns gave Miami a 14-6 halftime lead, and they appeared in control.
The Dolphins appeared ready to extend their lead when Williams broke loose for a 48-yard early in the third quarter, but the play was nullified when McMichael was called for holding.
A few minutes later, the secondary broke down and allowed David Carr to complete a 78-yard touchdown pass to Corey Bradford. After the Dolphins stopped Houston's two-point conversion attempt, they had a 14-12 lead.
Houston took a 15-14 lead after a poor Mark Royals punt set up the Texans in great field position and Brown kicked a 23-yard field goal.
The Dolphins regained the lead when Williams took Fiedler's pass and raced 35 yards to the end zone. The Dolphins went for a two-point conversion, but it failed when Fiedler's pass to a well-covered Travis Minor fell incomplete, leaving the score at 20-15.
Houston then put together a 16-play drive that culminated in a 24-yard field goal by Brown to make it 20-18 with just under five minutes left.
Then came Fiedler's costly interception on second-and-12 from the 29-yard line.
The Dolphins allowed Houston to run out almost all the clock when they let Stacey Mack gained 11 yards on a simple sweep on a third-and-7 from the Dolphins 33-yard line.
The loss snapped the Dolphins' opening-day winning streak at 11 games, which stood as the second-longest in NFL history behind Dallas' 17 straight.