World number four Zverev, defeated in his first singles match against David Goffin earlier this week, outclassed Vasek Pospisil 6-4 6-2.
Pospisil stuck with the Next Gen star for the majority of the first set before a looping forehand went long at 4-4 to hand Zverev the initiative, and the German completely controlled the second.
"I felt much better on court today," Zverev said. "A first match against Goffin was never going to be easy but I'm happy the way I played today.
"I served really well and played alright from the baseline, there's still plenty of work left to do."
Kerber remained unbeaten at the tournament with a 6-1 6-3 dismantling of Eugenie Bouchard, winning eight straight games from 1-0 down in the first set.
Bouchard mounted a mini comeback to level at 3-3 in the second, but saw four break points go begging as Kerber rallied once more to seal the win.
A 4-3 (5-2) 4-3 (5-2) victory in the mixed doubles rounded out a 3-0 triumph and means Germany can guarantee a spot in Saturday's final by beating Australia on Friday.
In Thursday's other contest, Belgium's Goffin kept up his own form with a 6-4 6-2 triumph over Australia's Thanasi Kokkinakis, and Elise Mertens recovered to beat Daria Gavrilova 2-6 6-4 6-2.
The Belgian duo then earned victory with a deciding set in the mixed doubles to maintain an outside chance of reaching the final.