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.
.
Britain's Dan Evans and James Ward both won their opening Australian Open qualifiers to move within two victories of the main draw.