Nick Kyrgios has sent Australia through to the Davis Cup semi-finals with an emphatic straight-sets win over American Sam Querrey in Sunday’s first reverse singles rubber.

Kyrgios prevailed 7-6 (7-4) 6-3 6-4, giving Australia an unbeatable 3-1 lead in the World Group quarter-final tie against the United States in Brisbane.

It is just the second time in the last 11 years Australia have made this stage of the competition, with a trip to Belgium or a home semi-final tie against Italy to come in September.