Abbi Grant was brought down in the box in the opening few minutes and Captain Leanne Ross stepped up to convert the spot kick.
It was a big moment for the City player after she heartbreakingly missed a penalty on Thursday night which would have seen City progress in the Champions League.
However, the City captain showed her quality and mental strength and buried the set piece.
It was 2-0 after 24 minutes when Noelle Murray converted past Megan Cunningham in the Celtic nets after good one two touch football between Katie McCabe and Jo Love, to set the striker up.
After the break Grant finished off another fine City move to make it 3-0 and Leanne Crichton smashed home on 65 minutes to make it a very comfortable afternoon for the reigning Champions.
Commenting, Glasgow City head coach Scott Booth said: “I am delighted with the three points.
"I am also really pleased with what I thought was one of the most professional performances we have given since I came to the club.
"We were really focused, played good football, were organised and had to dig deep given we put so much into Thursday’s European game.
"The experienced players made a big difference today.
"They kept things calm at the right times and helped us manage the game brilliantly.
"Four goals and a clean sheet today is very pleasing.”
The international break means that Glasgow City are next in action on Sunday, October 29 when Aberdeen come to Petershill Park. Kick off is 2pm.