Andy Guastaferro converted a 30th-minute penalty kick for the Americans (1-0-2), who finished second to the Cubans (2-0-1) in Group B and will face Costa Rica (3-0-0) in the semifinals on Friday.
Cuba will meet Mexico (2-1-0) in the other semifinal, with the winners advancing to the FIFA tournament Nov. 21-Dec. 5 in Chinese Taipei.
Costa Rica dominated Group A play, outscoring foes, 23-2. It finished group play Tuesday with a 4-0 victory over Mexico.
''I think that the pressure is on [Costa Rica],'' U.S. coach Keith Tozer said. ''They went to the World Cup in 2000 last time, it's their home building, it's their home country. Unlike Cuba tonight, they are going to have to come and attack us, and that is going to give us more room. Cuba just packed it in in front of their goal, whereas Costa Rica is going to have to come at us.
''I like our chances. I think with this team, anything can happen. We have guys who can score, guys who can defend and great goalies.''
Goalkeeper Scott Hileman made six saves as the Americans, missing captain Sean Bowers (calf injury) and John Ball (suspended for comments following his ejection in the group opener), created more chances in an otherwise even encounter.
Eduardo Morales fired Cuba ahead in the seventh minute from a Boris Saname feed on a counterattack.
Guastaferro, who also converted a penalty kick in Monday's 6-0 romp over Guyana, tallied after Danny Kelly was fouled in the Cuban penalty area.
The Americans would have qualified even with a one- or two-goal loss following Panama's 8-3 win over Guyana in the other Group B finale.
''It seems that we are getting better every game,'' Tozer said. ''As we expected, our defense has been keeping us in games. Scott [Hileman] had a really good game in goal, but the individual and the team defense was great.''
The United States finished third at the 1989 world championship, second in 1992 and 10th in 1996 but failed to qualify in 2000, when Costa Rica and Cuba joined host Guatemala as CONCACAF representatives. Brazil won the first three world titles and lost to Spain in the 2000 title game.
Futsal is a cousin of North American indoor soccer, featuring five-player teams on a basketball-like court with no walls and a low-bouncing ball. Indoor soccer features six-player teams and side- and backwalls on a hockey rink-sized field.
CONCACAF QUALIFYING TOURNAMENT
July 23-31 at Heredia, Costa Rica
U.S.
Schedule
July 24: United States 2 Panama 2
July 26: United States 6 Guyana 0
July 28: United States 1 Cuba 1
July 30: Semifinals, vs. Costa Rica
Aug. 1: Final/third place
Group A
W L T GF GA Pts
x-Costa Rica 3 0 0 23 2 9
x-Mexico 2 1 0 12 13 6
Trinidad & Tobago 1 2 0 12 16 3
Suriname 0 3 0
10 26 0
x - qualified for semifinals
Friday, July 23
Mexico 6 Trinidad & Tobago 4
Costa Rica 13 Suriname 1
Sunday, July 25
Mexico 6 Suriname
5
Costa Rica 6 Trinidad & Tobago 1
Tuesday, July 27
Costa Rica 4 Mexico 0
Trinidad & Tobago 7 Suriname 4
Group B
W L T GF
GA Pts
x-Cuba 2 0 1 13 4 7
x-United States 1 0 2 9 3 5
Panama 1 1 1 10
7 4
Guyana 0 3 0 6 24 0
x - qualified for semifinals
Saturday, July 24
United States 2 Panama 2
Cuba 10 Guyana
3
Monday, July 26
United States 6 Guyana 0
Cuba 2 Panama 0
Wednesday, July 28
United States 1 Cuba 1
Panama 8 Guyana 3
Semifinals
Friday, July
30
Costa Rica vs. United States
Cuba vs. Mexico
Third Place
Saturday, July 31
Semifinal losers
Championship
Saturday, July 31
Semifinals
winners
Note: Semifinal winners advance to Nov. 21-Dec. 5 FIFA Futsal World Championship in Chinese Taipei