Expansion franchise St Louis City's perfect start to their inaugural MLS season was ended by Minnesota United who triumphed 1-0 after Luis Amarilla's 78th-minute penalty on Saturday.
City had made MLS history by winning their first five games but that was ended by the Loons with Amarilla drilling home the spot kick after a needless challenge by Kyle Hiebert.
Hiebert brought down Amarilla just inside the box with a rash tackle when Jakob Nerwinski appeared to have Kervin Arriaga's wayward pass under control.
Substitute Samuel Adeniran came closest to equalising for St Louis, with a 95th-minute shot going over the bar after a great first touch from Klauss' right-wing cut back.
St Louis remain top of the table with 15 points from six games, but unbeaten Minnesota climb up to fourth in the Western Conference.
Cincinnati continued their impressive start to the season with a 1-0 home triumph over Inter Miami who slumped to their fourth straight defeat.
Yerson Mosquera scored the 45th-minute winner for Cincy, who are top of the Eastern Conference.
Giorgos Giakoumakis scored an early winner as Atlanta United moved up to second in the East with a 1-0 home win over New York Red Bulls, who are down in 12th in that conference.
Jordan Morris and Leo Chu scored first-half goals as Seattle Sounders stayed second in the West with a 2-1 victory at LA Galaxy, who are without a win and have only three points from five games.
LAFC remained unbeaten and third in the West despite a 0-0 draw at the winless Colorado Rapids, while SJ Earthquakes climbed to fifth with a 2-1 victory over Houston Dynamo with all three goals coming from penalties.
Vancouver Whitecaps snapped a run of three straight draws with a resounding 5-0 win over 10-man Montreal with Simon Becher scoring a double. Becher is the fastest player (87 minutes) in MLS history to score his first four goals.
Franck Boli rescued a 1-1 draw for Portland Timbers at Dallas, Chicago Fire and DC United drew 0-0 and Nashville triumphed 2-0 at Orlando City.
Federico Bernardeschi netted another spectacular goal with a strike straight from a corner in Toronto's 2-2 home draw with Charlotte.
Sporting KC remained winless after a 0-0 draw at Philadelphia Union, New England drew 1-1 with New York City and Real Salt Lake suffered their fourth straight loss, going down 4-0 to Columbus Crew.