Ostrava, Czech Republic (SportsNetwork.com) - Bernard Tomic posted a big win Sunday, as he gave visiting Australia an insurmountable lead in its' eventual 3-2 victory over the Czech Republic in an opening-round Davis Cup tie.

The Aussies headed into Day 3 with a 2-1 advantage in the best-of-five affair and the German-born Tomic propelled the visitors into the quarterfinals by besting Lukas Rosol 7-6 (7-4), 6-3, 7-6 (7-5) in 2 hours, 13 minutes at Cez Arena.

A dead rubber then saw little-known Czech Jan Mertl top Sam Groth, 6-3, 6-2.

The Czechs stayed alive on Saturday with a doubles victory by Jiri Vesely and Adam Pavlasek, this after Australia swept Friday's opening singles with victories by Thanasi Kokkinakis and Tomic, respectively, in Ostrava.

The three-time Davis Cup champion Czechs played this weekend without Tomas Berdych and Radek Stepanek. The veteran duo helped the host nation to consecutive titles in 2012 and 2013.

Australia has won 28 Davis Cup titles, but none since 2003. The Aussies hadn't advanced beyond the World Group first round since a semifinal run back in 2006.

The Aussies are now 7-1 versus the Czechs.

Next up for Australia will be visiting Kazakhstan in July.