On a surface offering little to the bowlers, Wagner bent his back and used the short ball to good effect as he took five for 31 in 16 overs.
As a result Zimbabwe went to tea on 120 for eight after they had won the toss and elected to bat first, with tailender Donald Tiripano's unbeaten 28 the highest score.
Zimbabwe had not played a Test since November 2014, and the hiatus showed in their inability to occupy the crease on a pitch that held no demons.
In a 13-over spell either side of the lunch break, the 30-year-old removed Chibhabha and Sean Williams before the interval and then struck three times in one over to reduce the hosts to 72 for eight.
All but one of his dismissals came from short deliveries, as Zimbabwe's batsmen had no answer to the tactic.
Left-arm spinner Mitchell Santner backed him up with the important wickets of Masakadza and Craig Ervine, registering figures of two for 12 from seven overs.
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