Sran was drafted into the India side following their embarrassing two-run defeat in Saturday's series opener, and marked his debut in the format with figures of 4 for 10 in four overs.
The left-armer's four wickets came in the space of seven deliveries in his first spell as Zimbabwe were reduced to 28 for four.
Bumrah did the damage at the back of the innings, as he dismissed top scorer Peter Moor for 31 and danger man Elton Chigumbura for eight to record figures of 3 for 11.
Zimbabwe went into the game buoyed by their much-improved performance on Saturday, as well as the hope of recording a rare T20 series win.
But after winning the toss and electing to bat, their batsmen put in the sort of desperate performance that brought a series whitewash in the three-match one-day international series.
The third and final Twenty20 international takes place on Wednesday.