It was fellow countryman Jorg Albertz who secured the priceless win with an 11th minute penalty but manager Dick Advocaat could scarcely have been through a more traumatic match for many years.
Reyna went for two yellow cards in the space of two minutes then Arthur Numan was booked for a foul on Robbie Neilson and then sent off for continuing to complain.
It meant that Rangers had to play the last 19 minutes with only nine men but, marshalled by the excellent Lorenzo Amoruso and the tireless Barry Ferguson they held on.
It now means, though, that both Reyna and Numan are automatically out of next Sunday’s home game with Motherwell and Amoruso starts a two-game ban after that.
Although the loss of the captaincy had a huge effect on Amoruso he has shown in the past week that when he is on form he is a quite excellent central defender.
He snuffed out Chris Sutton in the 5-1 mauling of Celtic and then performed quite brilliantly in Thursday’s 1-0 win over Kaiserslautern, not only defensively but also in the way he passed the ball.
He was a tower of strength against Hearts and it was his passing ability which enabled Rangers to take an early lead at Tynecastle.
The powerful Italian launched a wonderful 50-yard pass in 11 minutes which sailed over Steven Pressley’s head and sent Barry Ferguson scampering into the box on the left hand side.
Former Rangers defender Gordan Petric was caught short and made a lunging challenge on the Ibrox skipper and referee Stuart Dougal had no hesitation in pointing to the penalty spot.
The Hearts fans seem to feel that Ferguson had dived but there was little doubt about the award and Jorg Albertz slammed the spotkick low into the right corner, although Antti Niemi made a fair effort to get it.
It was everything Rangers deserved as they had started the match much brighter than Hearts, who were obviously keen to impress new manager Craig Levein who was paraded to the crowd before kick-off.
Ferguson was running the show in midfield and Ronald de Boer continued to show his improvement in form, linking the play so well just outside the Hearts box.
The Dutchman displayed this perfectly in 18 minutes with a super lay-off to Claudio Reyna and the American international drove a left foot shot which flew just over the bar.
However, for all of their early pressure Rangers could not build on their lead and Hearts came right back into the game towards the end of the first half.
There seems little doubt that Gordon Durie was keen to do well against his old club and he came desperately close to scoring with two efforts in the space of a minute.
Scott Severin’s cross in 27 minutes was deflected directly into Durie’s area and he sent a powerful downward header towards the right corner but Stefan Klos got across brilliantly to make a great blocking save.
Stevie Fulton swung over the resultant corner and the ball broke again for Durie.This time he let fly with his left foot but Klos was again equal to it with great smothering save.
Hearts were almost in again in 35 minutes and this time Durie was the creator as he sent strike Andy Kirk clear in the box but Klos was quick off his line ti the deny the Uisterman.
These were alarming moments for Dick Advocaat as Rangers had fallen out of the game but there was even worse to come in the second half when Rangers were astonishingly reduced to nine men in a torrid second period.
Bert Konterman and Jorg Albertz were booked for fouls on Durie and Juanjo as Rangers seem to lose their composure. Then, remarkably Claudio Reyna was sent off for two fouls in two minutes.
He was rightly yellow carded in 63 minutes for barging over Grant Murray. Then in 65 minutes he brought down Andy Kirk near the touchline and Dougal issused a second yellow and Reyna had to go off,
Ferguson was booked for complaining and Rangers suddenly had a real fight on their hands but there was even worse to come when Arthur Numan saw red in extremely controversial circumstances 19 minutes from time.
He was cautioned for a foul on Robbie Neilson and then was sent off by Dougal for offering dissent to the referee when lining up in Rangers’ defensive wall.
Rangers now had nine men but somehow Rangers managed to hang on although they had Stefan Klos to thank for a quite remarkable save three minutes from time which prevented an equaliser.
Andy Kirk’s header seemed destined for the the net when Klos incredibly blocked it with his left leg in mid-air. It was a save which could mean so much in terms of the championship.
It was traumatic at Tynecastle but Rangers got the win they needed to keep the heat on league leaders Celtic.
HEARTS: Niemi; Neilson, Petric (Milne 74), Pressley, Murray; Cameron, Severin (Tomaschek 82), Fulton, Juanjo; Kirk, Durie. Subs – McKenzie, Locke, McSwegan.
Bookings: Murray (21) Juanjo (36) Pressley (68)
RANGERS: Klos; Wilson, Konterman, Amoruso; Reyna, Ferguson, De Boer, Albertz, Numan; Flo (Tugay 72), Miller (80). Subs – Christiansen, McCann, Ross.
Sent off: Reyna (65), Numan (71) Bookings: Konterman (53) Albertz (59) Ferguson (65) Tugay (90)