Three of the five Scottish Premiership games on Saturday ended 0-0 as Rangers made it a disappointing start for Ian Cathro.
Rob Kiernan's first ever goal for Rangers and Barrie McKay's second-half strike condemned Ian Cathro to defeat in his first game in charge of Hearts.
Don Cowie thought he had given Cathro's side the lead in the first half only for the linesman to rule it out in a marginal call.
Ireland U21 international Kiernan then rose to nod in James Taverier's free-kick delivery and put the Gers in front.
McKay's second-half strike from close range ensured Hearts had a mountain to climb and they struggled to create much going forward as Rangers saw the game out with little fuss.
Elsewhere, former Manchester United youth player Larnell Cole ensured that Iverness secured a point against Hamilton in a game Caley Thistle boss Richie Foran will know they should have won.
Hamilton midfielder Ali Crawford gave Hamilton the lead after 16 minutes dispatching a free-kick from distance and it was a lead they took into half-time.
Cole scored early into the second half to draw Inverness level, smashing the ball into the top corner with a great strike but the Caley Jags failed to make their dominance count and grab a winner.
A second-half penalty decision also went against Inverness amid dramatic and frustrated appeals but referee Greg Aitken was unmoved .
The draw keeps Inverness off the bottom by a point but still in 11th position in the table while Hamilton sit in eighth, one point above Foran's men.
The three other games in the Scottish Premiership finished scoreless as St Johnstone ground out a 0-0 at Aberdeen and Dundee drew 0-0 at home to Ross County.
Motherwell also followed up last week's frenetic 4-3 defeat to Celtic at Fir Park with a 0-0 draw against Kilmarnock.