Davis' feed to the far post was headed in by teammate Brian Ching during first half stoppage time as the Dynamo defeated the Union, 1-0, to win the aggregate goal, two-game series, 3-1.
Houston had opened the series with Sunday's 2-1 win over the Union at PPL Park in Chester.
"He was the difference-maker in this series," Union defender Danny Califf said of Davis.
Thus, the Union's season ended where it started on March 19, when they opened with a 1-0 win over the Dynamo at Robertson Stadium.
Team manager Peter Nowak stayed upbeat after the playoff ouster. "We had a lot of things to be proud of this year," he said, "and this will be a lesson for us."
Nowak wasn't so upbeat about the call that awarded Davis his free kick. Union defender Carlos Valdes was called for fouling Calen Carr, thus giving Davis the free kick.
Nowak felt it wasn't a foul, that the half should have been over, and that there was too much stoppage time.
Valdes agreed about the foul.
"It was not a foul," he said.
The Union central defender then made a pointed comment about his team's inability to defend set pieces.
"We were confused when defending set pieces," Valdes said. "Sometimes we need to work on concentrating more."
Davis set the tone in Sunday's game on a similar play to his game-winner here. At PPL Park, he sent a free kick about the same 40-yard distance to be headed in by teammate Andre Hainault for the first goal of the first-leg win.
While some may suggest that David Beckham of the Los Angeles Galaxy is the most accurate MLS passer, Davis, who had 16 assists in the regular season, has clearly stated his case this year - and especially in this series.
What hurt the Union was that they continued to try to beat Houston with long passes and the Dynamo is too strong in the air for that tactic.
The Union had two new starters - midfielder Veljko Paunovic, who missed the previous two games with a hamstring injury, and Jack McInerney.
In addition, the Union also started Sebastien Le Toux at midfield instead of his more accustomed target spot up top and the team's leading scorer wasn't as effective in this second game after scoring in the first.
In the 59th minute, Paunovic unleashed a blast from just outside the box that went just over the goal for the Union's first true offensive chance in the second half.
Still trailing, 1-0, the Union went for firepower by using its three substitutions all at once in the 66th minute, bringing in Freddy Adu, Roger Torres and Justin Mapp.
Almost immediately, the Union began putting more heat on the Houston defense, but it wasn't long until the Dynamo settled down.
Throughout this two-game series the Union tried to attack with long balls, but that played to Houston's strength, because of the Dynamo's proficiency in the air.
Adu shot wide from just inside the box in the 87th minute in what would be the Union's last true scoring chance.
Contact staff writer Marc Narducci at 856-779-3225, firstname.lastname@example.org,
or @sjnard on Twitter.