Former Dungannon Swifts defender Hegarty clearly enjoyed his 40th minute header against Northern Ireland’s most successful club who were playing at Ibrox for the first time.
The 20-year-old had stated in his pre-match press conferences that he would love to score against his countrymen and he did just that with an accurate finish from a Fraser Aird delivery.
And with just a minute to go Murray Park starlet Murdoch, who had replaced Ian Black after the hour mark, tried his luck from 25 yards and his deflected shot spun over Linfield's substitute keeper Alan Blayney.
The result this evening, of course, was irrelevant as both sets of fans enjoyed this historic match and it was to be a special occasion for Gers teenagers Luca Gasparotto, Charlie Telfer, Daniel Stoney, Ryan Sinnamon, goalkeeper Alan Smith and scorer Murdoch as they all got their first taste of top team football in the second half.
The atmosphere generated by the crowd throughout was impressive but the opening stages of the game were played in midfield with neither team pushing forward with great intent.
Indeed it was not until the 11th minute that the first shot was attempted and it was from the visitors. Nathan Hanley’s deflected cross bounced in front of centre half Stephen Douglas but his effort from 20 yards soared into the Copland Stand.
On a night where a lot of substitutions are expected McCoist would not have been looking to make his first after just 16 minutes when Barrie McKay hobbled off and was replaced by Fraser Aird.
David Templeton was again looking lively early on and with his confidence high following his stunning double against Queen’s Park on Sunday he tried his luck from distance with a dipping right-foot shot which had to be watched closely by Ross Glendinning as it flew over his bar.
Temps was again playing in the hole behind Lee McCulloch and on 22 minutes he found space and teed up the skipper who tried to find the opposite bottom corner of the net but couldn’t get the required curl on his shot.
Rangers were looking the far likelier to get the opening goal and before the half hour mark Black had his hands on his head when his powerful left foot drive from distance went over after a good break down the left by Aird.
Linfield, however, were still in the game and a long ball from Douglas caused a bit of confusion between Lee Wallace and Emilson Cribari and Matthew Tipton’s snap shot flew across Neil Alexander and inches wide of the target.
On 39 minutes good link up play on the right between Ulstermen Andy Mitchell and Hegarty resulted in the latter playing a good cross into the danger area but Templeton couldn’t get his foot to the ball and it was booted clear.
It was not long, however, before Rangers got their noses in front and it was that man Hegarty who scored a dream goal.
The 20-year-old rose above the Linfield defence to power a header into the net and as he ran back to the half way line he looked over to his manager and both started a Gangnam Style dance to celebrate the moment.
For the start of the second period McCoist made three changes with towering Canadian stopper Gasparotto taking the place of Emilson Cribari in defence while Robbie Crawford and Kal Naismith slotted in for Kyle Hutton and Lee McCulloch respectively.
This did little to change the flow of the game with Rangers continuing to dominate and after Templeton had come close with an acrobatic overhead kick Black hit a stinging shot from 25 yards which was well saved.
Just before the hour mark there was more activity on the home bench with three more substitutions.
Argyriou went on for Lee Wallace while both Murdoch and Telfer were given firm handshakes from their boss and Kenny McDowall as they made their top team debuts.
Within minutes Jeffrey also made sweeping changes with several players given their chance to shine on the lush Ibrox turf and almost immediately the Belfast Blues had the ball in the net when their number 9 Peter Thomson glanced a great header beyond Alexander but the far side linesman quickly raised his flag for offside.
This resulted in a chorus of boos from the Linfield fans, and from the Rangers supporters as well!
There was to be more debuts handed out by McCoist with full back Sinnamon, goalkeeper Smith and winger Stoney getting 20 minutes and every one of the club’s rising stars looked composed on the big stage.
Linfield will have felt they should have equalised when Billy Joe Burns’ cross from the left was missed by sub Ryan Henderson who looked the favourite to head home from six yards.
But with just 60 seconds left Murdoch made it 2-0 when he picked up the ball and his 25 yard shot gave sub keeper Blayney no chance albeit he was aided by a deflection off a defender.
RANGERS (4-4-2): Alexander (Smith 70); Hegarty, Cribari (Gasparotto 46), Faure (Stoney 70), Wallace (Argyriou 61 (Sinnamon 70); Mitchell, Black (Murdoch 61), Hutton (Crawford 46), McKay (Aird 16); Templeton (Telfer 61), McCulloch (Naismith 46)
SUBS NOT USED: None