The Bombers kicked the opening goal of the third term, but when the Giants responded with the next three, the margin was out to 27 points.
Josh Green found the answering goal for the Dons when the side was able to get out the back of the Giants defence for one of the few times of the opening two and a half quarters.
Tom Bellchambers continued his strong showing. He had 36 hits outs in the first three quarters compared to Shane Mumford’s 22.
Essendon kicked 3.3 in the third quarter but the Giants made their opportunities count, kicking five straight to take a 25-point lead into the final change.
The Bombers kicked the opening two goals of the last quarter through Green and Travis Colyer to cut the margin to 13 points.
The Giants answered but the Dons weren't going away. Anthony McDonald-Tipungwuti's goal left the Dons 15 points down with ten minutes to play.
Just 30 seconds later, Walla had another and it was nine points the difference.
From the next centre clearance the Giants scrambled the ball forward and found the answering goal.
They were able to hold their nerve from there to record the win.
The Giants held a slight edge in the key statistical areas (clearances 39-33, inside 50s 53-44, contested possessions 126-115).
Zach Merrett (29 disposals), Jobe Watson (28) and Martin Gleeson (23) were the main ball winners.
Green was the leading goal kicker with three.