Scotland had gone 1-0 up in the series in Edinburgh on Wednesday, but Zimbabwe pegged them back to 1-1 on Friday and then took this third and final game in dramatic fashion.
Chasing 177 runs to win, Zimbabwe still needed 56 runs from the last 24 balls of their innings to win and it looked as if Scotland were in the box seat.
However, then Milton Shumba really went for it, hitting three sixes off the first three balls of the 17th over bowled by seamer Ali Evans.
He then got a single before Wessley Madhevere hit a six and, in total, 25 came off the over.
The put Zimbabwe in with a great chance – and when they hit 14 off Safyaan Sharif in the 18th over they then needed 17 runs from the final two overs.
They got them, getting home by six wickets with five balls to spare with Shumba being unbeaten on 66 off just 29 balls.
Scotland have to dust themselves down quickly now as they head off to Oman this week for Cricket World Cup League Two matches against the hosts and Papua New Guinea.
After that it is the T20 World Cup in Oman and the UAE and Coetzer said: “There is no doubt that the guys will see this as one that got away.
“A win was within our grasp and we let it go, we had set things up nicely with the bat, but then could not back it up with our bowling and fielding and that was frustrating.
“We had a chance to win a series against a good side though and that shows how nicely this squad is building towards the World Cup.
“The squad will now regroup and head to Oman and I am excited to lead this group of guys into big games coming up.”
Head coach Shane Burger added: “We are obviously disappointed with the way this series has ended, however, we take away plenty of positives from these three games.
“At times we have shown that our batting, bowling and fielding can fire - we just have to put the three parts together going forward when we are involved in high pressure games.”
Scotland won the toss and decided to bat first, Coetzer and Oli Hairs falling quite cheaply, but George Munsey was in excellent form, making 54 off just 30 balls before he was out.
Richie Berrington made 44 and then 30 runs came off the last over of the innings with, amongst other things, Calum MacLeod hitting a six, Michael Leask hitting two sixes and Richard Ngarava bowling two no balls.
MacLeod finished on 39 not out from 29 balls and Leask 17 not out off just five balls.
Zimbabwe’s innings then ebbed and flowed before Shumba’s heroics at the death.