After spilling 10 points in their first seven games, boss Steven Gerrard had warned the Light Blues they could forget about a championship challenge if they lost to the leaders.
But they fired themselves back into the chasing pack with a ruthless first-half display that saw Ryan Kent, Alfredo Morelos and Scott Arfield strike.
Hearts had kicked-off the campaign with six wins and a draw – but Rangers made easier work of Craig Levein’s men than they could possibly have expected.
On-loan Burnley defender Jimmy Dunne did head the visitors a consolation effort but they were already a man light by that point after seeing Michael Smith sent off early in the second period.
Rangers may only climb one place but they trim the deficit on Hearts to five points, leaving the Jambos with a lead of just two on city rivals Hibernian.
Gerrard went with the same starting line-up that recorded an impressive Europa League win over Rapid Vienna on Thursday while the visitors welcomed frontman Uche Ikpeazu back from injury.
But it was the hosts who picked up where they left off against the Austrians as they grabbed the opener within two minutes.
Peter Haring flattened Kent outside the box but while the Hearts backline stepped up as James Tavernier swung in the free-kick, Ikpeazu stayed deep playing Morelos onside.
Hearts appealed in vain but linesman Frankie Connor left his flag down as the Colombian unselfishly squared to Kent to slot past the exposed Zdenek Zlamal.
Levein’s men were furious but their mood did not improve as Rangers number one Allan McGregor pulled off two crucial blocks to deny Steven Naismith then Ikpeazu a swift reply.
Zlamal was also on his toes to deny Jon Flanagan but there was no rescuing Hearts in the 12th minute as Rangers doubled their lead.
Daniel Candeias robbed Demetri Mitchell and wasted no time rolling the ball across goal for Morelos to net with a cheeky back-heel flick.
It was a full-blooded contest with neither side shying away from a meaty challenge.
Ikpeazu threw his considerable weight about as he bounced Connor Goldson to the floor before bulldozing half the length of the pitch with Lassana Coulibaly at his tail.
As he looked to turn inside, the Mali international nicked possession but referee John Beaton saw nothing wrong with the tackle despite the Hearts striker’s appeals for a penalty.
Instead of finding a lifeline, it was game over after 32 minutes.
Tavernier’s cross from deep looked to be heading out but Morelos refused to give up the chase, craning his neck as he headed down for Arfield to slot home.
Some Jambos fans headed straight for the exit and those who remained behind saw their side reduced to 10 men nine minutes into the second period.
Smith had been booked early for a foul on Ovie Ejaria and collected his second with a body check on Flanagan.
Dunne got Hearts on the scoresheet in the 67th minute as he rose to nod home from an Olly Lee free-kick but the damage was already done.
Goldson almost gave his side a nervy finish when he gifted possession away but McGregor came up with a vital stop to deny Arnaud Djoum.