Morris and Spottiswood's catalogue of failings came to light when heavily pregnant Lorna MacDonald had her gas fire checked when her son was experiencing headaches.
The mother-of-three was shocked to find that during a renovation of her flat the chimney had been removed and there was debris left from the work.
She feared she could have come home from her nightshift and found her family dead.
Morris and Spottiswood, which was commissioned by Glasgow Housing Association to carry out work on the flat, pled guilty to breaching Health and Safety regulations.
Douglas Bennett, managing director, said: "The company accepts the court's judgment and apologises for not meeting our health & safety responsibilities in connection with this matter.
"Health and safety is our number one priority, and the safety of the public is carefully considered in everything we do. We are reassured by the court's recognition that the company is safety conscious and has a good safety record."
Ms MacDonald, 30, of Drumchapel, said: "I can't believe it. There has been so much hassle over the past couple of years.
"I am happy they have pled guilty. They weren't interested in helping us. They fixed the wall the chimney was on after two years."
Sheriff Bill Totten heard that Morris and Spottiswood had tendered to Glasgow Housing Association to carry out renovation work on the block of flats, where there was a mix of owner-occupiers and tenants. The project, which started in September 2008, included the removal of redundant chimneys to reduce future maintenance costs. Morris and Spottiswood sub-contracted the work to remove the chimneys, but had failed to provide sufficient direction and supervision to the sub-contractor. The family had been living in the flat since 2006 and the gas fire was in place in the house when they purchased it. They knew work was being carried out on their home but had no idea the chimney was being taken away.
The flat was visited at various times in early 2009 by a Morris and Spottiswood site foreman, a client-tenant liaison officer and a gas engineer to check the appliances when Ms MacDonald's mechanic partner, Colin Morrison was in. Mr Morrison said he was told the chimney was not to be removed.
The foreman had recorded that there was an electric fire in the property, when in fact it was a gas fire, which required the chimney for a flue.
Self-employed roofer and builder Thomas Smith carried out the work under the supervision and direction of the company.
Debris had also fallen down the chimney while the work was carried out as well as the chimney being capped. This combination resulted in the carbon monoxide from an active fire spilling back into the living room, which could have been fatal at high or prolonged exposure. Health and Safety Executive inspector Helen Diamond said: "This was, for the family, a potentially fatal combination of circumstances."