It was a welcome victory after a defeats to England and France. Glasgow's Ruaridh Jackson went over for a try in the Zimbabwe match.
Head coach Stephen Gemmell said: "The boys really dug in and played well. It's a great lift for the team to get a win ahead of tomorrow.
"I'm really encouraged by the progress that the team has made over the three games today."
You can watch the action from the Emirates Airline Dubai Sevens on BBC1 tomorrow.
1.05-2.00pm - All the rounds and Quarter Finals from that day.
Interactive, 2.00-5.30pm - semi-finals and finals - viewers need to press their red button to access this.