The Jambos have won all four meetings with Celtic and Rangers this season, sparking credible ambitions that they can become the first non-Glasgow side since Alex Ferguson's Aberdeen in 1985 to win the Scottish title.
The Edinburgh side have not won the top-flight since 1959/60.
Rangers had been unbeaten in eight league games since Danny Rohl took charge to rekindle their own title hopes, but were undone by two goals in four minutes just before half-time at Tynecastle.
Stuart Findlay headed in a well-worked corner before Lawrence Shankland embarrassed Jack Butland at his near post.
Derek McInnes' men then saw out the second half comfortably until an error from Frankie Kent allowed Youssef Chermiti to pull a goal back with virtually the last kick of the game.
Rangers fell 12 points behind the leaders, albeit with a game in hand.
Second-placed Celtic have played two fewer matches than Hearts but are in turmoil ahead of Aberdeen's visit to Parkhead later on Sunday.
New manager Wilfried Nancy has lost his first four matches in charge to oversee the Scottish champions' worst run since 1978.
