Boyd then sealed the victory with his 23rrd goal of the campaign and this was as comfortable a match as manager Walter Smith could have hoped for.
Now his team will face either Celtic or Dundee United at Hampden on March 15 as it bids to win the trophy for the 26th time in the club’s history.
Gers will find out who their opponents are when the other semi-final is played tomorrow night and whoever they face, they’ll have a hard task on their hands.
Old Firm clashes always capture the fans’ imagination while the Arabs are so far unbeaten in four games with Glasgow’s big two this season.
Either way, the fight for tickets is now underway after the Light Blues cantered to the last match of the competition.
Smith made three changes to the side which drew 0-0 at Aberdeen in the SPL on Saturday.
Back by popular demand was leading scorer Boyd and he joined Novo in a two-man attack.
Steven Naismith also started as he came in for John Fleck and the teenager dropped to the bench along with Lee McCulloch and Kenny Miller.
With Hampden only half-full, Gers had the first opportunity but Pedro Mendes’ effort on the volley was weak and always trundling wide.
Falkirk’s response was swift, with ex-Ibrox favourite Neil McCann threading through to the dangerous Steve Lovell.
The former Aberdeen hitman had opened the scoring when these sides last met in the league and it seemed he might do so again as he homed in on goal.
But Allan McGregor, back to his best in recent weeks, came out to meet his man and spread himself really well to make a crucial save with his left boot.
Not content with that, the Gers number one made another fine stop from Lovell seconds later as the Bairns looked to capitalise on Kirk Broadfoot’s mistake.
It was a shaky start from Smith’s men and it’s unlikely the manager would have been too happy with the way his team had begun.
But his mood will undoubtedly have improved after eight minutes when Novo pounced to put Rangers ahead.
The Spaniard’s perseverance helped him win a corner and when Mendes drilled it in from the left, Madjid Bougherra rose to nod it on.
Boyd was first to react but while he couldn’t get the touch he needed to score, Novo was there to scramble in at the back post.
The SPL title challengers pushed for a quick second and Mendes dispossessed his man but Novo’s drive only spun off the Portuguese midfielder and behind for a goal kick.
Naismith was then blocked and when Barry Ferguson lifted the rebound to Boyd, his overhead kick crept across the frame and wide.
Gers were starting to enjoy more of the ball and were certainly creating the better opportunities.
But after Naismith was unlucky to see Novo’s defence-splitting pass smothered by keeper Dani Mallo, it took late intervention from Broadfoot to stop McCann from levelling.
Falkirk were trying to lift themselves after an awkward period when they were having clear problems with the uneven surface.
But after McCann won a corner, Kevin McBride shot past and that gave Rangers a chance to edge upfield again.
Naismith nearly made it 2-0 after Boyd held off Steven Pressley’s attentions and Mendes almost saw his effort bundled over the line by Mallo but it stayed out.
Once more Naismith looked like breaking his duck for the season with a crisp volley after a poor Mendes corner but it whistled a yard beyond the far post.
As half-time approached, Gers knew doubling their advantage would leave them in a commanding position at the midway point.
And after Mallo stopped a Boyd piledriver, the Light Blues – playing in their red third strip – moved further ahead when Novo got his second.
Davis was the architect, sending a brilliant ball through the right channel for the little forward to latch on and fire across the keeper to net.
That left John Hughes’ team with everything to do in the second period and with Novo on a hat-trick, they faced a man determined to get it.
He had his first opportunity to hit the treble mark less than three minute in but his well-struck shot flew agonisingly wide.
Back came Falkirk, who forced another excellent save from McGregor when Darren Barr’s header looked to be sneaking in.
Scott Arfield also had a go with a measured volley but it rose inches too high and Rangers were let off the hook.
Naismith tried to breathe life into the game as it started threatening to fizzle out and his lung-bursting run from defence won a corner.
But although Gers wasted the set-piece – as they did all too often over the piece – it made little difference overall.
Davis, like Naismith, had the crowd cheering with another good dash towards goal and his shot was diverted just wide.
The only trouble was that such moments were few and far between as Falkirk seldom looked like getting back into contention.
Rangers continued to look more potent and Boyd’s scissor kick bounced into the ground then touched the bar on its way over after Novo’s assist as they came upfield again.
Mendes had one last try at scoring but while some of his touches had been a joy to watch, he clearly didn’t have his shooting boots on.
With the clock running down, John Fleck came on for the tiring Naismith and he gave Boyd a great chance of getting on the scoresheet.
He couldn’t hit the target then but did two minutes from the end when he tackled Mallo to win the ball and roll into an open goal.
That put gloss on a great night’s work by Rangers and now they can look forward to the final with confidence just under two months from now.