Dzumhur struggled early on, losing five games on the bounce and only marginally recovering in a one-sided opening set Down Under.
He swept aside the challenge of Damir Dzumhur, the No 28 seed of Bosnia, in one hour and 50 minutes with a 6-1, 6-3, 6-1 victory.
Women's No. 19 seed Magdalena Rybarikova made it through Kateryna Bondarenko in three sets, 7-5, 3-6, 6-1.
The 49th-ranked Edmund fought back taking the last two sets in blistering heat to win 7-6 (7/0), 3-6, 4-6, 6-0, 7-5 in 3hr 34min on Show Court Two.
When and where will be the Australian Open 2018 be played?
"The things that I need to improve, the matches will give me that, no?"
The win took the 31-year-old Spaniard's Australian Open record to 53-11 as he chases his second Australian title after beating Federer in the 2009 final. Shes a very experienced player and shes very long time on tour, said the Latvian. "Let's see how far I can go".
Im very happy to be back, its a very important beginning for me.
Extreme heat has caused troubling levels of exhaustion and heat stress for the players at the Australian Open, but more concerningly for the people in the state of Victoria, Australia where several people have died to the sweltering conditions. The other men's top-10 seed was Pablo Careeno Busta, who comes in at No. 10 and who needed four sets to beat No 23 Gilles Muller, 7-6 (4), 4-6, 7-5, 7-5.
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