Goals from Kenny Miller and Haris Vuckic put Rangers into a commanding position but, after being reduced to 10 men following Lee McCulloch’s red card, they endured a nervous finish to the game after Genero Zeefuik had cut the deficit with a late header.
Stuart McCall’s team are now three points clear of third-placed Hibernian and still have a game in hand on the Easter Road side.
The home side gave Hearts a guard of honour onto the pitch as an acknowledgement of their championship triumph but the respect ended as soon as the first whistle blew.
Nicky Law forced Neil Alexander into a save in the first two minutes of the game after collecting a corner on the edge of the box as the home side attempted to make a brisk start to the contest.
Hearts were only sporadically able to pass the ball with the speed and purpose which has become their trademark during a glittering campaign, instead conceding lots of possession to a hard-working Rangers side.
At no point did they play like champions, either when the game was an 11-against-11 contest or when they had an extra man after McCulloch’s 43rd-minute dismissal for an elbow.
Jamie Walker cut inside onto his favoured right foot before unleashing a shot narrowly beyond Cammy Bell’s left-hand post in the champions’ first meaningful attack of the game, and that after 20 minutes of play.
Goalscoring chances had been few and far between when Miller made his mark in the 28th minute, applying a clinical first-time finish to Ross Wallace’s low cross after the left-back had advanced into a deep attacking position.
The goal did little to spur Hearts into action but injected an extra level of confidence into Rangers, who had doubled their advantage within nine minutes.
On-loan Newcastle United winger Vuckic was given too much time on the ball in the visitors’ box and glided past Kevin McHattie with ease before striking a firm left-footed shot into the far corner.
Rangers, though, were forced into a reshuffle two minutes before half-time when their skipper McCulloch was sent off after leading with an arm when competing for a header with Hearts striker Osman Sow.
Vuckic was selected to make way for centre-back Bilel Mohsni during the interval to ensure the back four remained intact.
The man advantage did little to help Hearts and in fact it was Rangers who almost scored the game’s next goal, Miller striking a tame shot straight into Alexander’s hands when unmarked in the penalty area.
Dutch striker Zeefuik was the man in the right place at the right time to tap home after Bell had kept out Sow’s header to set up the grandstand finish with eight minutes to go.
Hearts overloaded in attack during that period but Rangers remained resolute and saw out a well-deserved victory.
As a result, McCall’s side move into the top spot in the play-off places and the victory, against the division’s clear winners, will only enhance confidence at Ibrox that a place in the Scottish top flight can be secured.