The 21-year-old from Beverley enjoyed a successful season last year, reaching the fourth round of the US Open, and winter training with British No 1 Sir Andy Murray paid dividends on Monday.
It took Edmund two hours and 10 minutes to dispatch Californian hopeful Escobedo 7-6 (7/4) 7-6 (8/6) at the Queensland Tennis Centre. He will next face either sixth seed Lucas Pouille or Gilles Simon.
Johanna Konta dropped just two games in her opening match of the new season to progress in the Shenzhen Open in China.
Konta had finished the 2016 campaign inside the world’s top 10 and she picked up where she left off with a comfortable 6-2 6-0 first-round victory over Turkey’s Cagla Buyukakcay in under an hour. “I’m really happy to have started the year again, and I’m really enjoying my time in Shenzhen,” said Konta.
Elsewhere, Roger Federer marked his long-awaited comeback from injury with a confident straight-sets victory over Dan Evans to help Switzerland defeat Great Britain in their Hopman Cup opener.
The 35-year-old Federer needed only an hour and three minutes to dispatch Birmingham’s Evans 6-3 6-4 in Perth. Belinda Bencic then secured an unassailable 2-0 lead in the tie for the Swiss with a 7-5 3-6 6-2 victory over Heather Watson in the women’s singles.
It was Federer’s performance that grabbed the attention though, as he showed little sign of rust despite missing six months of action with knee and back problems.