Evans lost his serve just once as he beat Italian top seed Luca Vanni 7-6 (7-5) 6-4, and he will face Israel's Amir Weintraub in the second round.
Ward sent down 16 aces in a 7-6 (8-6) 6-4 win over Canada's Peter Polansky.
Elsewhere, Nick Kyrgios suffered a pre-Open scare when he pulled out of his opening match at the Kooyong Classic.
The 20-year-old Australian handed Belgian David Goffin victory as he retired with a foot injury. He later tweeted that it was precautionary.
The year's first Grand Slam starts in Melbourne on Monday.
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The leaks from a secret BND report suggest that its monitoring station at Bad Aibling spied on France's presidential palace and foreign ministry, and the European Commission.
The US National Security Agency also allegedly spied on some European firms.
German Interior Minister Thomas de Maiziere denies claims of a cover-up.
The BND reportedly collected information on European firms at Washington's behest to check if they were breaking trade embargos.
According to the reports, the BND did not target German or US officials in the surveillance, as they are protected by a BND-NSA agreement signed in 2002.
However, it has emerged that the German government knew about NSA spying on European arms businesses as early as 2008. The government found "shortcomings" in the BND's operations, German TV reports.
Minister under pressure - by the BBC's Jenny Hill in Berlin:
Yesterday the tabloid newspaper Bild printed a picture of Interior Minister Thomas de Maiziere - his nose elongated to Pinocchio proportions.
"Herr de Maiziere!" the accompanying headline screamed. "You lie with impunity!"
There's outrage here that Germany - for so long seen as the victim of American espionage - may have helped US spies to target other Europeans. And pressure is building on the government to reveal how much it knew.
As the former minister in charge of the chancellery, Thomas de Maiziere was directly responsible for Germany's foreign intelligence agency, the BND, in 2008.
And that is when, it's claimed, the BND first told the chancellery that its agents were now helping the NSA to spy on European aviation, aerospace and defence companies.
Mr de Maiziere has denied all knowledge, and maintains that he hasn't deceived anyone. But he says that - because the information is all classified - he is unable to comment publicly.
Yet there are questions about who else was aware. Another German newspaper devoted its front page to a "wanted" poster. Among the mugshots of politicians and civil servants was Chancellor Angela Merkel herself.
Spy scandal turns tables on German government
Mr de Maiziere denies having had any knowledge of malpractice at German intelligence.
But he called for the internal BND report to be presented to a parliamentary committee, "the sooner the better".
The huge scale of NSA surveillance in Europe - including joint spying operations with the UK's GCHQ - was revealed in 2013 by US whistleblower Edward Snowden.
There was outrage in Germany because of the scope of NSA spying, which allegedly included snooping on Chancellor Merkel's mobile phone conversations. The revelations strained German-US diplomatic ties.
Last July Germany expelled a CIA official based at the US embassy, as reports surfaced of several Germans having spied for the NSA.
Germany's leftist Die Linke party accused the German government on Wednesday of "lying" in connection with NSA activities.
German media reports speak of NSA attempts to spy on Airbus and Eurocopter, now known as Airbus Helicopters, via the BND.
Britain's Dan Evans and James Ward both won their opening Australian Open qualifiers to move within two victories of the main draw.
[NEXT_CONCEPT]
Germany's national intelligence agency, the BND, spied on top French officials and the EU's headquarters on behalf of US intelligence, German media report.