Red hot Lemponye Tshireletso's first half brace at the National Stadium in Gaborone was decisive for the Zebras.
Botswana put in a virtuoso performance and had chances to score more goals but failed to convert their many chances as they ran rings around a disjointed Bissau defence.
Lemponye who was in superb form was a constant threat as he broke the deadlock with a fine finish on the half hour mark before completing his brace seven minutes later as the Zebras went to the break leading comfortably.
The second half was a see-saw affair as Guinea Bissau fought hard to limit the damage holding the maurauding Zebras until the end as the hosts won comfortably.
The second leg will be played on the 3rd of August 2014.