Kyle Edmund of Great Britain, pictured in March 2018, achieved his best Estoril showing. (AFP/CLIVE BRUNSKILL) |
De Minaur is based in Spain and clay is his favoured surface but he had few answers as Edmund advanced in 97 minutes.
Edmund, ranked a career-high 23rd, achieved his best Estoril showing after losing in the second round last year to Benoit Paire.
"I felt really good with how I played throughout," the third seed said. "I faced a tough opponent, who is very resilient.
"He didn't give away a lot of points, I had to work for this win. But I enjoyed winning a tough test, delivering in a pressure match.
"I've trained with Alex. I know he has a difficult game. He likes to counter-attack and use the pace to deflect.
"I knew how the match would go. I had to execute and impose my game to win it."
The Briton will next tackle Portuguese number one Joao Sousa, who needed two and a half hours to knock out namesake and compatriot Pedro Sousa with a 4-6, 7-6 (7/1), 7-5 win.
Edmund broke De Minaur five times as he played for the first time since a first-round loss in Monte Carlo.
De Minaur, 19, is still alive in the doubles alongside his 37-year-old Davis Cup captain Lleyton Hewitt.
The field in Portugal is headed by US Open runner-up Kevin Anderson, with the South African to start his campaign on Thursday against Greek rising star Stefanos Tsitsipas, the losing finalist last weekend to Rafael Nadal in Barcelona.
Second round results:
Kyle Edmund (GBR) bt Alex de Minaur (AUS) 6-2, 7-5
Joao Sousa (POR) bt Pedro Sousa (POR) 4-6, 7-6 (7/1), 7-5
Frances Tiafoe (USA) bt Gilles Muller (LUX) 6-4, 7-5
Simone Bolelli (ITA) bt Federico Delbonis (ARG) 3-6, 7-5, 6-2
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