The Scots upset the odds in unforgettable fashion by beating the West Indies in their opening match, but a loss against Ireland meant they faced a winner-takes-all decider to close out Group B.
A lack of runs cost them as they mustered just 133-6, but they made a game attempt to defend on a sticky, worn surface.
Craig Ervine (58) and Sikandar Raza (40) chalked off the majority of the target but Mark Watt and Josh Davey removed both set batters at the death to force a close finish.
In the end Zimbabwe required just six from the last two overs and got there with nine balls to spare.
Michael Jones and Matthew Cross both fell cheaply in the powerplay but, just as he had done against the West Indies, George Munsey provided some much-needed steel.
He made a workmanlike 54 off 51 deliveries and received some support from Calum McLeod's 25, but there was no real sense of momentum.
Scotland responded with two quick wickets of their own, Davey and Brad Wheal both successful in their first over.
But a fourth-wicket stand of 64 between Ervine and Raza dragged Zimbabwe into a healthy position.
Davey and Watt held their nerve to prise out the experienced pair before the job was finished, but Zimbabwe finished well to join the likes of India, Pakistan and South Africa in Group 2.