Anderson downed Johnson 6-4, 7-6 (10/8) to give himself an excellent chance of claiming his third career ATP title in a severely weakened field.
The world No16 is the only remaining player in the top 20 and the only one to win an ATP title, with none of his rivals even making a final on the tour before.
The situation arose after five seeded players withdrew from the Australian Open warm-up event, four of them without even lifting a racquet, and the remainder of the top-ranked competitors were eliminated by less-fancied rivals.
It leaves 28-year-old Anderson, seeded fourth coming onto the tournament, as the most experienced player in the semi-finals, although his opponent on Friday Jirí Veselý will be no pushover.
The Czech qualifier took Anderson to five sets at last year's Australian open, only succumbing after almost four hours.
The other semi-final is an all-French affair between Lucas Pouille and Adrian Mannarino, who have never met before.