After wins on Wednesday for Colin Fleming and Ross Hutchins and Londoner Dominic Inglot and his Filipino partner Treat Huey, Murray and Peers triumphed 7-6 (7/4) 7-6 (8/6).
In the second round they will play Murray's former partner, American Eric Butorac, and South African Raven Kaasen, who put paid to the comeback of Pat Rafter alongside Lleyton Hewitt in round one.
However, the Australian Open finally implemented its extreme heat policy as temperatures once again rose over 40C in Melbourne.
Whether to put the policy into effect is this year entirely at the discretion of tournament referee Wayne McKewen after a change in the rules.
McKewen uses the Wet Bulb Globe Temperature reading, which takes into account humidity and wind direction as well as heat.
He had been criticised for allowing play to continue throughout Tuesday and Wednesday despite temperatures soaring above 40C.
Canadian Frank Dancevic and a ball boy both fainted on court, three players withdrew mid-match because of the effects of the heat and spectators left in their droves.
At just before 2pm local time on Thursday, the announcement came that the policy had been implemented, with the temperature measured at 42C.
Play did not stop immediately, with all players required to complete the set they were playing.
The roofs on Rod Laver Arena and Hisense Arena would then be closed before play resumed, while matches on uncovered courts would only start again once conditions were deemed safe.
It was quickly announced that would not be before 4pm, but the expectation was it would be later than that, with temperatures in Melbourne often not peaking until early evening.
On Tuesday the highest reading at Melbourne Park was 42.2C at 5.45pm.
There has been a mixed reaction from the players, with many accepting the decision not to stop, but Dancevic branded being made to play in such conditions "inhumane" while Ivan Dodig, who retired from his match on Wednesday, said he feared he might die.
Fourth seed Andy Murray, meanwhile, warned the tournament not to take undue risks.
Following his first-round match against Go Soeda, the Scot said: "It looks terrible for the whole sport when people are collapsing, ball kids are collapsing, people in the stands are collapsing. That's obviously not great.
"There's been some issues in other sports with players having heart attacks. I don't know exactly why that is. In this heat, that's when you're really pushing it to your limits. You don't want to see anything bad happen to anyone."
Varvara Lepchenko was the main victim on Thursday, the American taking a medical time-out during the second set of her second-round match against Simona Halep.
Lepchenko lay down across two chairs while a doctor examined her and had ice rubbed over her body before continuing. Having won the first set she managed only one more game in a 4-6 6-0 6-1 defeat.