Edmund, who had never previously gone past the second round before in Melbourne, swept aside Istomin in straight sets – 6-2, 6-2, 6-4.
The Brit went into the match full of confidence after knocking out 11th seed Kevin Anderson in a gripping five-setter on Monday.
And he was rarely troubled against Istomin.
The Uzbek looked off the pace from the outset, while Edmund was in control.
Edmund was dominant with his big serve and his depth got him out of trouble on big points.
The Uzbek looked off the pace, while Edmund was in control.
He was faultless and averaged 67 per cent of his first serves in.
With 38 winners to boot too, Edmund was unstoppable.
And he took the match on serve when Istomin fired his backhand long.
Speaking after his win, Edmund said: “There is always that danger of someone like Denis coming back – you saw what he did here last year (knocking out Novak Djokovic).
“It was a professional performance and doing it quickly will do me good.
“The plan is to get through, whatever it takes – if it takes three or four hours then so be it, but it’s perfect really.”