Andy Roddick needed just an hour and 40 minutes to beat Razvan Sabau in straight sets and assure the United States victory over Romania in their Davis Cup first-round World Group tie.
Roddick, unwell on Friday when he lost to Andrei Pavel in five sets, easily beat huge underdog Sabau, the world number 112, 6-3 6-3 6-2.
The triumph gave the US a decisive 3-1 lead - they would later make it 4-1 - and means they will now take on Chile, who knocked out last year's beaten finalists, Slovakia.
Victor Hanescu was supposed to be world number three Roddick's opponent but he pulled up with an injury in Saturday's doubles and had to retire from that clash to give the US a 2-1 lead.
The United States are looking for their first Davis Cup title since 1995 when a team consisting of Pete Sampras, Jim Courier and Todd Martin beat Russia in Moscow.
Australia needed five rubbers but they finally saw off Switzerland in their first-round tie with Chris Guccione beating George Bastl to propel the Aussies forward.
The tie lacked the glamour it would have had with Roger Federer not in the Swiss line-up and Lleyton Hewitt not playing for the Australians.
Stanislas Wawrinka had evened the tie for the Swiss in the day's first singles rubber with a 6-4 6-2 6-7 (5-7) 6-2 triumph over Peter Luczak.
Guccione clinched a last-eight place for the visitors, however, with a 7-5 6-3 7-6 (9-7) win over Bastl, whose biggest claim to fame is his first-round win against Pete Sampras at Wimbledon in 2002.
Next up for Australia are Belarus, who needed just two days to beat Spain in their first-round clash.
They wrapped up a 4-1 win by sharing the reverse singles on Sunday in Minsk.
David Ferrer netted a hollow triumph for Spain when he beat Serguei Tarasevitch 6-2 6-1, with the match reduced to best-of-three sets as the outcome was not riding on it.
Vladimir Voltchkov then ensured a comfortable margin of victory for Belarus by seeing off Tommy Robredo 7-6 (8-6) 6-3 in the final rubber.
Holders Croatia had ensured a place in the last eight on Saturday by taking a 3-0 lead against Austria in Graz and will next play at home against an Argentina team that also secured victory by winning the doubles rubber against Sweden in Buenos Aires on Saturday and taking a 3-0 advantage.
In the first of Sunday's singles Argentina stretched that to 4-0 as Juan Ignacio Chela beat Thomas Johansson 6-4 6-1 and Gaston Gaudio made it a clean sweep with a 6-0 6-1 win at the expense of Jonas Bjorkman.
Meanwhile, Croatia player-captain Ivan Ljubicic rested himself and Mario Ancic from Sunday's dead rubbers and watched the stand-ins surrender both dead rubbers to leave the final score 3-2 in favour of the defending champions.
First Ljubicic watched Ivo Karlovic be beaten by Alexander Peya 4-6 6-2 6-4 as Austria pulled back to 3-1 and then Stefan Koubek saw off Marin Cilic 6-1 7-5.
The team that lost to Croatia in December's final, Slovakia, were eliminated at the hands of Chile whose Olympic gold medal-winning doubles team of Fernando Gonzalez and Nicolas Massu saw off Lukas Lacko and Michal Mertinak in the doubles at Rancagua to render Sunday's reverse singles meaningless.
France will play Russia in the quarter-finals with those teams seeing off Germany and Holland respectively with a day to spare.
Russia extended their supremacy by winning both Sunday singles to triumph 5-0.
Igor Andreev beat Jesse Huta-Galung 6-3 4-6 7-6 (9/7) before Dimitry Tursunov downed Melle van Gemerden 7-6 (7/4) 7-6 (7/5).
Germany won both dead rubbers on Sunday to ensure the final score was 3-2 to France at Halle with Rainer Schuettler earning a 6-4 6-3 victory at the expense of Arnaud Clement before Tommy Haas dispatched Michael Llodra 6-3 6-3.