Temperatures in the Highlands dipped as low as -15 degrees celsius overnight making for frosty conditions for the lunchtime kick-off in Dingwall.
However, Brendan Rodgers' men shrugged off the cold and the absence of top scorers this season Nicolas Kuhn and Daizen Maeda due to injury.
With James Forrest and Luis Palma also missing, Rodgers had just one fit winger to choose from in Yang Hyun-jun.
Furuhashi was therefore deployed in an unfamiliar wide right role but proved just as effective in front of goal when he turned in Alistair Johnston's cross five minutes before half-time.
County levelled on the hour mark through Jordan White's penalty after Johnston bundled over Kieran Phillips.
Goalkeeper Jordan Amissah then kept Celtic at bay until Furuhashi stooped to head in Arne Engels' cross 10 minutes from time.
Engels then sealed the points in stoppage time with a twice-taken penalty after Amissah came off his line in saving the Belgian's first attempt.
Luke McCowan added a fourth in the 98th minute as Celtic took another step towards a fourth consecutive league title.
Second-placed Rangers are not in action until Sunday when they host St. Johnstone.
Gers' boss Philippe Clement was backed by the club's new CEO Patrick Stewart on Saturday despite winning just one of his last five games.
"I need to make some tough decisions, it comes with the role, but I am committed to making the right ones for Rangers, not just the popular ones," Stewart said as he addressed media for the first time.
"So cutting to the chase, we are backing Philippe at this time as a board."