After two successive draws the Gers faced an important test against their SPL championship rivals from Edinburgh.
The home team came through with flying colours thanks to two goals from Boyd early in the second half.
Boyd was just one of four changes to the starting line-up made by French boss Paul Le Guen as the Gers sought to get their title challenge into gear after a misfiring start.
Swedish defender Karl Svensson's header from Chris Burke's cross was well held by Craig Gordon and the Hearts keeper again saved well from a Boyd header.
Hearts threatened briefly when Joao Morais Bruno Aguiar's well struck free-kick was touched over by goalkeeper Lionel Letizi before Rangers wasted a chance when Julien Rodriguez headed over another dangerous Lee Martin cross.
Gordon was performing heroics for Hearts as he raced from his line to block Dado Prso's shot and then reacted well to touch over Boyd's clever overhead flick.
Just before half-time the Hearts keeper parried Prso's first effort, but was helpless as Boyd looked set to roll the rebound into the empty net before Robbie Neilson popped up to clear off the line.
However, Rangers caught Hearts out with two goals inside the first five minutes of the second half.
Prso cleverly drifted past Neilson in the box only to be brought down by the wing back and Boyd despatched his spot kick powerfully into the net, sending Gordon the wrong way.
Shortly after, from Martin's well-flighted free-kick, Boyd was left unmarked at the back post and headed home a simple goal to double the lead and at last give the Ibrox faithful reason to be optimistic.
It was almost three after a shocking Panagiotis Fyssas mistake in trying to intercept Boyd's pass found Prso, whose first time 20-yard shot came back off the woodwork.
Hearts' discipline cracked under the relentless Rangers pressure and Neilson saw red in the final minutes for a second bookable offence.