Falkirk, though, frustrated the hosts until that flurry of goals around the hour mark.
Alistair Johnston dispossessed Calvin Miller before curling into the far corner; 22-year-old centre-half Dane Murray marked his new contract by heading his first Celtic goal; then substitute Yang Hyun-jun's low cross deflected in off Falkirk defender Liam Henderson.
Henderson had almost passed into his own net early on, former Celtic goalkeeper Scott Bain saved well from Tierney and McGregor, while an Arne Engels free-kick slammed off the face of the far post, all before Maeda's breakthrough.
Falkirk's failure to win either of their opening league fixtures has had some fearing their ability to compete in the top flight, but they did pose a threat of their own on the break.
Ross MacIver stabbed wide a chance to open the scoring, while Miller forced a fine save from Viljami Sinisalo and Alfredo Agyeman shot straight at the goalkeeper as the visitors sought an equaliser.
The game was over as a contest by the time they did become the first side to score against Celtic this season and what a beauty it was - Keelan Adams marking his 50th Falkirk appearance by thundering a drive home from the edge of the box.