The two-time former champions were shocked by Scotland in their opening match but kept their hopes of reaching the Super 12 stage of the tournament alive in Hobart on Tuesday.
Defending a target of 154, Joseph produced a fiery spell as the Carribean outfit eventually dismissed their opponents for a total 122 with 10 balls to spare.
Windies captain Nicholas Pooran had won the toss and opted to bat but they were pegged back by a disciplined Zimbabwe bowling performance, batting out the 20 overs for a total of 153-7.
Johnson Charles top-scored with 45 from 36 balls before he was comically run-out and then the West Indies lost four wickets for 11 runs in 12 balls with spinner Sikandar Raza taking 3-19 in his four overs.
A late innings flourish from Rovman Powell (28 off21 balls) and Akeal Hosein (23 not out off 18 balls) saw the Caribbean side get over the 150-run mark.
Zimbabwe were fast out of the blocks in the run-chase, taking 18 runs from the first over bowled by Kyle Mayers.
Joseph though came into the attack and was immediately into the wickets when Regis Chakabva (13) dragged the ball onto his stumps.
The paceman took his second with a lightning delivery to remove Tony Munyonga (2) and Sean Williams (1) fell two balls later as the pressure began building for Zimbabwe.
Jason Holder also chipped in with figures of 3-12 before Joseph came back to shatter the stumps of Luke Jongwe (29) to end any hope Zimbabwe had.
The result mean all four teams sit on two points and one win after two matches in the group with Friday's final round of games a winner takes all affair.
West Indies take on Ireland while Zimbabwe play Scotland with only two teams reaching the next stage of the global tournament.