Paul Le Guen made four changes to the side that faced Dunfermline at East End Park last weekend with Bardsley, Burke, Boyd and Martin replacing Hutton, Sionko, Buffel and Adam respectively.
And the Gers, who made a positive start to the match, could have taken the lead after only two minutes.
Chris Burke darted in from the right wing and found Boyd in the 18-yard box. The striker’s lay off to Clement was perfect but the Frenchman blazed his effort over the bar.
Within the opening ten minutes, Svensson and Rodriguez also called Craig Gordon into action with excellent headers.
With both teams desperate to pick up three points from this afternoon’s fixture the early stages were, as expected, played at an unbelievable tempo but it was riveting viewing for both sets of supporters.
Hearts, who started the match with an attacking 4-3-3 formation, were pushing forward at every given opportunity and Bruno Aguiar was unlucky with a dipping free-kick which was tipped over by Letizi on 11 minutes.
With the play flowing from end to end, Rodriguez would have been disappointed not to open the scoring when Lee Martin produced a pinpoint cross from a corner and the big defender, who was unmarked, headed over from 12 yards.
Rangers were clearly in the mood after disappointing draws against Dundee United and Dunfermline and Dado Prso should have scored on 21 minutes when he received a pass from Boyd in the box but could only watch on a Gordon made a great save with his legs.
Boyd then had a spectacular effort of his own when he found a yard of space in the danger area and flicked the ball up before attempting an overhead kick that Gordon palmed over the crossbar.
Despite the relentless pace of the game, referee Kenny Clark controlled the game well and was correct to pull out his first yellow card of the afternoon to Julien Brellier for a cynical foul on Chris Burke.
Rangers were without doubt the better of the sides in what was a pulsating 45 minutes of football but they were unable to find the net although they had yet another great chance with only seconds remaining.
Burke scooped the ball through to Prso and when Gordon saved his effort bravely, Boyd then had an effort blocked on the line by Robbie Neilson.
Le Guen will have been disappointed that his side could not take the lead before the interval but he must have been more than satisfied with the performances of on-loan stars Martin and Bardsley who looked confident and assured on their home debuts.
If Boyd was guilty of missing a snip just before the interval the SPL’s top scorer in 2005/06 made no mistake when Rangers awarded a penalty within the opening 60 seconds of the restart.
Dado Prso was brought down in the 18-yard box by Neilson and Kris showed great composure to send Gordon the wrong way.
The Rangers fans erupted and they were in heaven when the club’s goalscoring machine scored a second before the 50-minute mark.
Lee Martin supplied yet another dangerous cross into the six-yard box and Boyd showed his predatory instinct to head the ball home from close range.
At this point the atmosphere in Ibrox was electrifying and the boys in Light Blue were clearly starting to enjoy themselves.
Burke and Martin were showing some neat flicks and tricks but Paul Le Guen was quick to come out of his dug-out to make sure complacency was not about to creep into his team’s play.
Dado Prso, who was captain on the day, must have been wondering where his luck has disappeared to on 58 minutes when Boyd passed the ball to the Croatian after a mistake from Takis Fyssas and his spectacular effort from 25-yards smashed off the post with Gordon well beaten.
Le Guen was forced to make his first substitution of the match on 66 minutes when Barsdley limped off and Alan Hutton took his place.
The Salford-born defender was rightly given a standing ovation as he left the field and immediately put ice on his ankle before making his way up the tunnel.
Le Guen made a further change four minutes later when he decided to give Filip Sebo a run-out and the Slovakian, who scored a hat-trick for his country against Malta during the week, replaced man-of-the-match Kris Boyd.
With a commanding lead already in place, Rangers started to slow the game down and Clement and Hemdani were outstanding as the Light Blues attempted to maintain possession.
In the end, neither team created many clearcut chances in the final 15 minutes but this took nothing away from what was surely one of the most entertaining matches at Ibrox in a long time.
Hearts started to show a bit of frustration at the latter stages and Robbie Neilson was sent off for a second bookable offence on Lee Martin in the final minute of the game.
RANGERS: Letizi; Bardsley (Hutton 66), Svensson, Rodriguez, Smith; Burke (Buffel 87), Hemdani, Clement, Martin; Prso, Boyd (Sebo 70)
Subs Not Used: McGregor, Rae, Sionko, Adam
Bookings: None
HEARTS: Gordon; Neilson, Pressley, Berra, Fyssas; Mikoliunas (Hartley 66), Aguiar Brellier; Jankauskas, Bednar (Pospisal 45 (McCann 61)), Elliot
Subs Not Used: Banks, Wallace, Karipidis, Mole
Bookings: Yellow – Brellier (25) Pressley (79) Fyssas (83) Red – Neilson (90)
Referee: Kenny Clark
Attd: 50,239
Man of the Match: Kris Boyd