Romain Grosjean and Kevin Magnussen finished fourth and fifth in Austria, albeit lapped, for a 22-point bonanza that lifted Haas to 49 points and five ahead of former champions McLaren.
The double points result was only the third in the Ferrari-powered team's history.
"We had some luck in the race with the Mercedes cars not finishing but it’s been a great weekend and we can really build on that," said French driver Grosjean, who had not scored a point in his previous 12 races.
The Mercedes cars of Lewis Hamilton and Valtteri Bottas both retired while Red Bull's Daniel Ricciardo was also a non-finisher.
"We’ve shown this weekend that we’ve got a good car. Actually, it’s not only this weekend -- we’ve shown all year that the car is very competitive. We’ve just got to keep going like this," said Denmark's Magnussen.
(Reporting by Alan Baldwin, editing by Clare Fallon)
