The Hoops moved to the brink of a 12th title in 13 years thanks to Furuhashi's sharp first-half double.
Rangers can reduce the gap when they host Kilmarnock on Sunday.
But victory for the home side in next weekend's Old Firm clash at Celtic Park would realistically retain the title thanks to Celtic's superior goal difference.
"There was real energy in the stadium and the supporters were brilliant for us - the players responded to that," said Celtic boss Brendan Rodgers.
"What really pleased me today was, in a big game, we had big performances and big contributions from those players.
"That sets us up well for next week."
Hearts had beaten Celtic in their previous two meetings this season but were undone after just four minutes.
The visitors failed to clear from a corner and Furuhashi stooped to head in Reo Hatate's cross.
Furuhashi's second on 21 minutes owed much to a superb through ball from Matt O'Riley that the Japanese striker stroked home first time on the volley.
Hearts captain Lawrence Shankland had been a thorn in Celtic's side, scoring in all three prior encounters between the sides this season.
But it was a handball from the Scottish international that allowed O'Riley to smash home the third from the penalty spot late on and extend Celtic's goal difference advantage over Rangers to eight.
At the bottom of the table, Livingston's six-year stay in the top flight came to an end after a 4-1 thrashing at Motherwell.
Theo Bair scored twice for the steelmen, who are now safe.
Ross County moved out of the relegation playoff after coming from a goal down to beat Hibernian 2-1.
St. Johnstone are second from bottom after losing 1-0 at Aberdeen.
St. Mirren are in pole position to qualify for Europe for the first time since 1987 after a 3-1 win at Dundee.
Alex Gogic, Scott Tanser and Toyosi Olusanya were on target for the Buddies, who are now five points clear of Dundee in the battle for fifth.
