The world No2, who finished runner-up to Nicol David in 2013, won 11-7, 6-11, 11-9, 5-11, 11-9 against Egyptian teenager Nour El Sherbini.
Massaro, 30, said: "Nour played so well and I was nervous throughout the whole match. That's the hardest match I've ever played in my life.
"To hold the British Open and World Open titles in the same year - it's just dream stuff."
Men's world champion Nick Matthew plays his Canary Wharf Classic first round match tonight against Scotland's Alan Clyne.