The U.S' decision to try and gain an advantage over the Central Americans by playing in a cold climate and at altitude, looked in danger of back-firing and causing a major logistical headache but despite the snow blowing for 90 minutes, the game was able to be finished.
The Costa Ricans, though, were furious at the end of the game with their head coach Jorge Luis Pinto saying it was an "embarrassment to football" that the referee allowed the game to be played in such conditions.
Costa Rican officials said their federation would protest to FIFA about the referee's decision to continue with play in heavy snowfall.
The three points were vital for Jurgen Klinsmann's team after they lost their opening game of the qualifiers last month to Honduras and the German was delighted with the character his team showed in a blizzard.
"It was a snow battle," said Klinsmann, "We started really well, in the second half it was really a battle for second balls, for both teams it was tough to create a good passing game or chances," added the former Germany striker and coach.
"Overall it was great character shown by the team, they fought for every ball and did everything they could to adjust to those conditions," he added.
Klinsmann had named Dempsey as his new captain and the Tottenham Hotspur striker proved to be a decisive figure.
The Texan forward went close with a long-range effort moments before he put Klinsmann's team in front.
SNOW
Jozy Altidore tried his luck from the edge of the area and his shot deflected off Costa Rica defender Roy Miller and fell kindly to Dempsey who simply slotted home.
Dempsey raced to the crowd in a furious celebration, perhaps a release after a week dominated by denials of rumours of discontent between the players and their coach.
There was certainly no sign of anything but determination from the U.S as they battled in increasingly tricky conditions as the snowfall intensified.
German-born midfielder Jermaine Jones was an immense presence in midfield, setting the tone with his hard running and tackling.
Costa Rica, though, offered a reminder of their attacking potency in the 38th minute when Bryan Oviedo tested American keeper Brad Guzan with a fierce 20-yard drive but the home side went in 1-0 up at the break.
The game looked to be in doubt when the referee halted play in the 55th minute but after consultation and a few minutes of clearing the touchlines of snow, the match resumed.
Costa Rica piled on the pressure with Alvaro Saborio forcing Guzan into action with a diagonal shot in the 60th minute and two minutes later Michael Umana had a header disallowed for offside.
The Central Americans enjoyed the greater pressure throughout the final stages of the game but the U.S' makeshift defense held firm to claim the three points and a major morale boost.
The U.S, who have three points from two games, now play Mexico on Tuesday at the Azteca Stadium.
