Today's win marks Rangers' fourth win out of four against the Tynecastle men - indeed the Ibrox men have yet to concede a goal in 360 minutes of play.
Manager Alex McLeish made four changes from the starting line-up that had won at Dunfermline seven days ago with Kevin Muscat, Bob Malcolm, Claudio
Caniggia and Michael Mols replacing Maurice Ross, Craig Moore, Neil McCann and Shota Arveladze against a Hearts side containing two ex-Rangers' players Steven Pressley and Steven Boyack.
The home side kicked off in the knowledge that with Celtic's game at Motherwell postponed they had a clear and certain opportunity to extend their lead in the
Championship race - doubtless many Celtic fans joined the left-wing rabble demonstrating in Glasgow.
Rangers might have taken the lead in thirteen minutes when Caniggia's header from a Mikel Arteta free-kick flew across the face of goal.
Lorenzo Amoruso's free-kick at Dunfermline had obviously given him great encouragement (as if he needed any) for in nineteen minutes he powered in a
low drive from a similar dead-ball position - this effort whistling inches wide of the upright.
Sixty seconds later a superb crossfield pass from the Italian found Fernando Ricksen, whose cutback was sliced wide by Muscat with Barry Ferguson in prime
position.
The Stadium erupted in anger in 23 minutes when Ronald De Boer had the ball in the net only for the far-side linesman to chalk it off for offside. It all started
when Ferguson released Caniggia through the middle. The Argentinian was onside, whilst De Boer played a passive offside role. Caniggia should have scored himself, but saw his effort parried by goalkeeper Tepi Moilanen, De Boer converting the rebound - only for a late flag to chalk it off. The decision was correct - although Referee John Underhill could easily have awarded a penalty for Alan Maybury's foul on Caniggia.
If that decision was controversial - although correct - there was uproar four minutes later when Caniggia was sandwiched between Maybury and Pressley for a clear penalty. Unbelievably Referee Underhill waved play on.
Hearts had scarcely bothered the home defence - but on the half-hour mark Jean Louis Valois tested Stefan Klos with a 25-yard left-foot shot that 'Der Goalie' touched over.
In a game where no fewer than six visiting players were yellow-carded, Alan Maybury could consider himself fortunate not to receive a card of a sharper
colour in 35 minutes for a blatant body-check on Caniggia - yet Underhill contented himself with a lecture.
All was forgiven five minutes later however when Arteta's free-kick from wide on the left was headed into his own net by Scott Severin.
Michael Mols should have added a second nine minutes into the second-half when he was through on an Arthur Numan pass only to see his effort diverted wide.
Hearts again were fortunate to remain at full strength on the hour when Mols, through on a Ricksen pass, was hauled back by Andy Webster. Even though the defender was the last man he received only a yellow card.
Two minutes later Maybury at last saw yellow for a foul on Numan.
Peter Lovenkrands made a welcome return after a month's absence through injury - replacing Caniggia in 62 minutes.
Barry Ferguson might have secured the vital second seven minutes later when he turned on a Muscat cross only to scoop the ball high over the bar.
The 49,459 audience were now increasing in their collective nervousness as the clock ticked on with just the one goal advantage - even more so in 71 minutes when substitute Shota Arveladze played a one-two with Ronald De Boer only to miss-kick his shot wide.
Rangers continued to press - four minutes later a De Boer volley from an Arteta cross produced a fine save from Moilanen.
Hearts had barely threatened Klos' charge all afternoon, yet in the very last seconds of injury time a Severin free-kick broke to Mark De Vries whose shot
seemed goal-bound until Amoruso threw himself into the path of the ball to block it, Muscat effecting the clearance.
The final whistle sounded immediately afterwards for Rangers' second successive one-goal victory over Hearts.
Manager Alex McLeish afterwards reflected:
"We had a terrific first-half with Mikel Arteta more like his old self. We created lots of chances, but at 1-0 it's never finished. It's a concern that we're not
finishing teams off. Hearts threw caution to the wind late on."
RANGERS Klos; Muscat, Amoruso, Malcolm, Numan; Ricksen, Ferguson, Arteta, Caniggia (Lovenkrands 62); De Boer, Mols (Arveladze 68)
UNUSED SUBS McGregor, Eggen, Hughes
HEARTS Moilanen; Maybury, Pressley, Webster, Mahe; Severin, Boyack (Simmons 71), MacFarlane (McKenna 71), Valois (Kirk 84); De Vries, Wales
UNUSED SUBS Gordon, McCann
REFEREE John Underhill
Attendance 49,459