More than 4,600 people backed a campaign to save the X1 Hamilton to Glasgow link.
That followed The Scotsman being the first media to report the threat to the service on 20 September.
First Glasgow announced it would be withdrawn on 27 October, but the operator said it would keep running for another three or four months.
The operator said it would introduce some lower fares "as a last resort attempt to boost the service" but warned its future would be reviewed again if passenger numbers did not increase.
Politicians welcomed the move.
Hamilton, Larkhall and Stonehouse SNP MSP Christina McKelvie said: “I was absolutely delighted to hear from First Bus that the X1 route will continue up until Christmas.
"Being able to do my part to help the local campaign to save the X1 has been an incredibly rewarding experience."
“At my meeting with First, I explained to them the real damage the removal of the service would do to those working and studying in Glasgow.
"Alongside this, I raised the disproportionate number of concessionary users on the route, which is a stark indicator of the social link the route provides for many older residents.
“The local community deserve a huge amount of praise for this decision, as without the pressure from them this victory would not have been possible.”
Central Scotland Labour MSP Monica Lennon said: “It’s a massive relief that First Glasgow has responded to public pressure and will no longer proceed with axing the X1 Hamilton to Glasgow service this month.
"Our vital bus service is safe until the end of the year.
“Over 4,600 have signed the petition to save the bus and I’d encourage people to keep signing it.
"The next few months will be critical and we still have a lot to do to ensure the X1 is saved for good."
Lanark and Hamilton East SNP MP Angela Crawley also welcomed the development, having written to First Bus on behalf of many concerned constituents.Ms Crawley said: “The X1 route is a vital link between Hamilton and Glasgow, and for many residents is the cheapest and most efficient service into the city.
“I have heard from students, workers and pensioners who regularly use this service, with genuine concerns about how its cancellation would impact them financially and in terms of convenience.
First Glasgow commercial director Graeme Macfarlan said: “Service X1 is a route that has been in decline for a number of years in terms of passenger numbers, despite a number of efforts to make the route attractive to service users.
"The removal of any service is always the absolute last resort in this scenario and something we do not take lightly.
“Despite the numbers involved in the very public petitions against the removal of this service, we are simply not seeing this level of customer volume actually using the service.
"This must change if the service is to have a long-term and viable future as a commercial service, but we have taken on board the strong views of the paying public and local stakeholders who we have met with.
“As a result, we have taken the decision to reinstate the service as of 27 October.
"This registration has now been accepted by the Traffic Commissioner’s office, meaning there will be no gap in service from a customer’s point of view.
“The hope now with the service is that we may now in time see a boost to passenger numbers given the level of public and political support for the service.
“We will be looking to further support the service with a promotional and fares package in the coming weeks as a last resort attempt to boost the service.
"Should this not transpire over the next three or four months, then the future viability of the service will once again be under review.”