The 20-year-old Tiafoe, ranked 91st in the world, defeated 46th-ranked Canadian Denis Shapovalov 7-5, 6-4 to reach his first final.
Gojowczyk defeated American Steve Johnson 7-6 (7/3), 6-3.
Tiafoe's semi-final victory came hours after he finished off eighth-seeded South Korean Chung Hyeon 5-7, 6-4, 6-4 in a quarter-final halted by rain the night before.
Tiafoe led that match 5-3 in the third when play was halted, and the players were kept until after midnight before organizers decided to postpone the finish until Saturday.
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Tiafoe took control against Shapovalov with a late break in the first set, closing out the frame with an ace.
He won the first three games of the second before Shapovalov converted his only break chance of the match to make it 3-1.
Still up a break, Tiafoe steadied and closed out the contest in 71 minutes, finishing it out confidently with a love game.
He and 64th-ranked Gojowczyk will be meeting for the first time in an ATP Tour match, although they have split a pair of non-tour contests.
He saved the only break point he faced against Johnson, and said a more aggressive style that he has been cultivating is paying off as he continues to rebuild in the wake of foot surgery in 2014.