Wagner used his raw pace and intimidating short-pitched bowling to claim the wickets of Chamu Chibhabha and Sean Williams, as Zimbabwe limped into the lunch interval on 49 for four.
The hosts lost Brian Chari to the second ball of the day after they had won the toss and elected to bat, but then found stability in an hour-long partnership between Chibhabha and Hamilton Masakadza.
Wagner went to lunch with figures of two for eight from seven overs, while Craig Ervine and Sikandar Raza Butt were the two not-out batsmen for Zimbabwe.
Along with Prince Masvaure, both Chari and Chibhabha were making their Test debuts for Zimbabwe, who have not played a Test match since November 2014.
