Davis, who was part of the United States' FIFA World Cup campaign, played for Houston for the first time since mid-May and ensured his team secured a 2-2 draw with New York Red Bulls by slotting an 81st-minute spot kick at BBVA Compass Stadium.
Dynamo had taken the lead in the opening minute through Giles Barnes but the Red Bulls' in-form striker Bradley Wright-Phillips struck a brace to put the visitors in front with 19 minutes remaining.
The hosts ended a five-game losing streak, however, after New York midfielder Chris Duvall was judged to have handled the ball in the area, allowing Davis to do the rest.
The result means the Red Bulls have only won one of their past seven games in the MLS.
Barnes gave Houston the lead with just 39 seconds on the clock on Friday, heading Kofi Sarkodie's well-weighted cross into the net.
The English striker saw a similar header drift over the bar after 11 minutes and a minute later Wright-Phillips equalised for the visitors, running onto Eric Alexander's ball over the top and then rifling his shot past Houston goalkeeper Tally Hall.
In the 71st minute, Red Bulls left-back Ambroise Oyongo turned Andrew Driver inside out on the left and then picked out Wright-Phillips, who glanced his header into the far top corner and New York led.
The goal was Wright-Phillips' 14th of the season and took him three clear at the top of the MLS' golden boot standings.
But 10 minutes later, Davis struck and Dynamo moved up to 18 points and seventh in the Eastern Conference, while the fifth-placed Red Bulls have 20.
In California, more late drama saw Los Angeles Galaxy claim a 2-2 draw with Portland Timbers.
Portland's Rauwshan McKenzie put the ball in his own net with four minutes left to give the Galaxy a point.
LA hit the front four minutes past the hour mark when Marcelo Savas curled his shot past Donovan Ricketts in the Timbers' goal but the visitors responded almost immediately when Diego Valeri smashed a loose ball into the net in the 67th minute.
Portland claimed the lead four minutes later through Jorge Villafana but the Timbers failed to hold on for victory with McKenzie knocking Baggio Husidic's cross into the net in the closing stages.
The draw leaves the Galaxy in sixth position in the Western Conference standings with 21 points, just ahead of the Timbers on games won.
In other results, Real Salt Lake claimed their first league victory in six games, overcoming New England Revolution 2-1, Colorado Rapids drew 1-1 with Columbus Crew and FC Dallas defeated Philadelphia Union 2-1.
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