Kohlschreiber, 35, broke world No. 13 Fognini twice in both sets on his way to a comfortable 6-3, 6-1 win. The German, who won the ASB Auckland Classic in 2008, will face Tennys Sandgren in the final four after the American defeated Leonardo Mayer 6-3, 7-6 (5).
Norrie fired 11 aces and saved all four break points he faced during the match, breaking his opponent in the penultimate game of the second set to wrap up the win. Norrie will face Fritz at the Australian Open next week after the players were paired during the first-round draw on Thursday.
Struff advanced following a three-hour contest against No. 4 seed Pablo Carreno Busta. Struff won two tiebreaks as he edged the Spaniard 7-6(5), 6-7(5), 7-6(7).