Rangers brought their wretched run of Hampden defeats to an end as Steven Gerrard reached his first cup final as manager of the Ibrox club.
There was no immediate relief for Hearts from their recent miserable run of form as they were comprehensively beaten in their first match since sacking Craig Levein as manager.
Filip Helander’s goal in first half stoppage time set Rangers on their way before an Alfredo Morelos double after the break - taking the Colombian striker’s tally for the season to 20 - saw them ease their way into a first League Cup Final in nine seasons.
After losing on their previous six visits to Hampden, including a run of five semi-finals without scoring, this was the kind of emphatic win Gerrard needed to back up the improvements he has undoubtedly made since taking charge of Rangers.
The acid test is still to come with holders Celtic awaiting Gerrard’s men in the final on 8 December, the first Old Firm showpiece since Rangers won their last major honour in that 2010-11 League Cup Final.
It was an afternoon which did little for interim Hearts boss MacPheee’s hopes of landing the job on a permanent basis.
MacPhee’s decision to omit Uche Ikpeazu from his starting line-up raised a few eyebrows, given the significant discomfort the big striker had caused the Rangers defence at Tynecastle two weeks earlier.
It was a selection MacPhee was forced to revisit sooner than he would have wished with Ikpeazu introduced to the fray before half-time as a replacement for Steven MacLean who was teetering on the brink of a red card.
MacLean had been offered little opportunity to justify his presence up front for Hearts who spent most of the afternoon on the back foot.
While it was a nervy start to the contest from both sides, Rangers quickly established territorial dominance. But it took Gerrard’s men some time to find fluency and incisiveness in the attacking third of the pitch.
Ryan Kent carried the greatest degree of menace and invention for Rangers as they imposed control of possession. The £7 million winger created a couple of early openings for Morelos and Sheyi Ojo but both efforts were poor and failed to force Hearts goalkeeper Joel Pereira into action.
Hearts were grateful to Michael Smith’s awareness and position sense when the defender made a great interception to prevent Morelos getting on the end of a James Tavernier cross as Rangers built some momentum.
Pereira had to make his first save of the afternoon in the 19th minute when he did well to keep out Ryan Jack’s shot, then Smith was in the right place at the right time once again to block an effort from Glen Kamara.
MacLean made his way into referee John Beaton’s notebook in the 23rd minute when he was penalised for leading with an arm in an aerial challenge with Connor Goldson.
Hearts were grimly sticking to their task, often with 11 men behind the ball, and Pereira made another decent save to deny Tavernier who had been played in by Jack.
MacPhee was forced into his first change before the half hour mark, Glenn Whelan pulling up injured and replaced by Andrew Irving.
Sean Clare was booked for a late and lunging foul on Borna Barisic before referee Beaton was presented with a big call to make on MacLean. As Hearts forced their way into an attacking position for the first time, the striker appeared to leave a boot in as he challenged Allan McGregor.
The Rangers goalkeeper was incensed but after taking time to calm the situation, Beaton decided against a second yellow card for MacLean and decided a stern warning would suffice.
It was enough to prompt MacPhee to withdraw MacLean and send on Ikpeazu. Hearts looked to be on the brink of holding out until half-time, riding their luck as Kent struck the outside of Pereira’s left hand post with a fine shot and then Steven Davis saw an effort deflected narrowly wide.
But Hearts’ failure to properly defend the corner resulting from Davis’ attempt proved costly as Helander put Rangers ahead as the first half ticked into stoppage time. The Hearts defence were flat-footed as Morelos swept the ball back into the penalty area from the right and Helander stepped unchallenged into space to drive a left foot shot beyond Pereira.
There was still time before the interval for Hearts to force McGregor into his first save of the day but Ikpeazu’s tame effort was comfortably dealt with by the veteran ‘keeper.
Rangers were more than worthy of their lead and they doubled it two minutes into the second half.
Borna Barisic’s cross from the left picked out Ojo who was unable to direct his header towards goal. But the ball fell kindly for Tavernier who swept it back across the six yard box to give Morelos a simple tap-in.
Hearts passed up a couple of good chances to pull a goal back, both from corner kicks which left the Rangers defence looking uncertain, but Ikpeazu’s header was blocked by Jack before Craig Wighton wastefully headed wide from close range with the goal at his mercy.
Rangers removed any lingering doubt about the outcome when they made it 3-0 in the 62nd minute. Kent’s pace, directness and clever footwork carved out the opening down the left and his cross was brilliantly finished by Morelos who guided a left foot shot beyond Pereira’s right hand.
Pereira spared Hearts from a heavier defeat, making a fine double save to keep out substitutes Jermain Defoe and Scott Arfield in closing stages witnessed by very few Hearts supporters, most of whom had already made their excuses and left.