In what was a terrific match Danny Wilson opened the scoring after only four minutes with a well placed header beyond Jamie MacDonald.
Hearts, however, showed great character and Suso Santana made the most of an uncharacteristic error from Sasa Papac to blast the Jambos level.
Rangers regained their lead before the interval when Kenny Miller bagged his 18th goal of the season and three vital points were secured on 48 minutes when Steven Naismith notched a third with an accurate left-foot finish.
And Naisy capped a fine performance when he powered home a header with 16 minutes left to give Walter Smith’s team a comprehensive away victory in the capital.
In total Walter Smith made five changes to his side with Lee McCulloch, Steven Davis, Kevin Thomson, Kris Boyd and Kenny Miller replacing Fleck, Little, Lafferty, Beasley and Edu.
In defence Steven Whittaker, David Weir, Danny Wilson, and Sasa Papac again formed a formidable barrier in front of Allan McGregor’s goal.
And in the middle of the park Davis started on the right with McCulloch and Thomson, who made his 100th appearance for Rangers, returned to their central roles.
Up front the prolific partnership of Kris Boyd and Miller was again asked to find the net but it was Danny Wilson that gave the visitors the perfect start after only four minutes.
A free-kick midway in to Hearts half was delivered by Thomson in to the 18-yard box and despite the swirling wind inside the stadium the Gers starlet rose majestically to head the ball across MacDonald in to the net.
It was a fantastic moment for the youngster who was a threat from set pieces while coming through the Murray Park ranks.
Hearts had the ball in the net two minutes later when Gary Glen produced a fine finish beyond McGregor but the linesman had already raised his flag.
The 20-year-old striker was lively in the early stages and he then tested McGregor with a powerful shot from a wide angle after he had skipped past Wilson.
The home side recovered well from going behind and on 16 minutes they were on level terms.
Zaliukas flighted a long pass in to the box and when Sasa Papac skewed his clearance Suso Santana blasted a stunning volley which gave McGregor no chance.
Almost immediately Rangers looked to regain the lead and on 18 minutes Davis moved to the left flank and after cutting inside he swerved a great shot in to the opposite top corner but MacDonald was there to make a brilliant one-handed stop.
It was great stuff from both teams with the game being played at a breakneck speed and every player pushing forward with intent at every given opportunity.
With the half hour mark looming it was Hearts that were in the ascendancy although they again had MacDonald to thank after he darted from his line to deny Boyd before tipping an accurate curling effort from Miller.
On 30 minutes Rangers had their noses back in front and it was a terrific goal.
Davis found Boyd with a raking pass and he nodded it down in to the path of Naismith who sprinted through the middle of the Hearts defence.
His shot from 10 yards smashed off the bar but with MacDonald grounded Miller was there to head the ball in to the empty net.
Despite the bumpy playing surface this was a hugely entertaining first-half with both sides showing great passion and commitment.
In fact Naismith had to be calmed down by his teammates after a brief altercation with the Jambos’ winger Santana who was a stand-out in the opening 45 minutes.
Rangers again started the second-half positively with Wilson showing fantastic composure to link up with Davis in midfield before spraying a delightful pass to Boyd who was offside.
And just like first-half Smith’s team again scored early to increase their advantage.
Steven Whittaker darted in from the right and he found Naismith sprinting down the left unmarked.
He took one touch to compose himself before cleverly dinking the ball over MacDonald to find the net.
The goal could not have come at a better time but in this end-to-end encounter McGregor had to be alive to make a stunning stop in front of the ecstatic Rangers fans.
Santana delivered a pin-point corner kick and when Zaliukas angled a header towards the top corner Greegs had to be at his very best to palm the ball over.
Smith made his first change on 63 minutes with Mo Edu replacing Lee McCulloch, the manager clearly protecting his combative midfielder who had earlier been booked.
And on 76 minutes the scoreline was 4-1 and again it was Naismith that produced the goods.
Thomson again swung in a great free-kick in front of the Gers dug-out and the club’s no 14, who was unmarked, glanced a terrific header beyond MacDonald who was left grasping at thin air.
If anyone had any doubt about Rangers desire to win the title they only had to watch this 90 minutes to see that this is a side determined to get the job done as quickly as possible.
All over the park the players in blue were superb and rarely have the Rangers fans seen a better performance at Tynecastle.
Man of the Match – Tough one to call but Steven Naismith just edges it ahead of Danny Wilson.
His work-rate was excellent and it was great to see him rewarded with two superb goals.