Murray needed just over an hour and a half to despatch Robin Hause 6-3, 6-1, 6-3, with Tomic cruising through in three sets too against Leonardo Mayer.
Murray is aiming for the record books as he attempts to become the first man to follow up his debut grand slam title with a title in the next slam competition.
“I started the year well in Brisbane but coming into the Slams, the first match is normally pretty tough,” Murray said of his first match out in Melbourne.
“There are nerves in the build-up. You’ve just got to try and focus and play solid, not make too many silly mistakes.
Photo: Getty.