The Australian Open champions, seeded fourth in Monte Carlo, sealed victory in 67 minutes.
The Briton and the Brazilian went 4-0 up in the opening set and held firm to remain top of the ATP doubles rankings.
A reflex Murray volley sealed the match and improved their season record to 17 wins and only three defeats.
In the final they will meet either Pierre-Hugues Herbert and Nicolas Mahut, who beat Murray's brother Andy and Dominic Inglot on Friday, or Juan Sebastian Cabal and Robert Farah.
Brazilian Melo would have regained his individual number one doubles ranking with victory alongside Dodig of Croatia.
But the second seeds, playing in their first semi-final of the year, were unable to take any of their four break points and decisively lost serve in the ninth game of the second set.
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Sannah Javid, 26, of Frank Slater House, Green Lane, Ilford, was taken to King George Hospital on Tuesday after officers were called to her flat.
She died in the early hours of Wednesday. Post-mortem tests found the cause of death was multiple injuries.
Metropolitan Police detectives believe Ms Javid knew her attacker.
The force said a 37-year-old man was arrested on suspicion of her murder on Saturday.
Det Ch Insp Tim Duffield added: "We are appealing for anyone who may have seen or heard something suspicious on the evening of Tuesday, 2 December to call the incident room at Hendon."

The tiny identity tags are essentially tiny imperfections in the building blocks of matter, making them virtually impossible to clone.
They could be used as the basis of a robust system for authenticating hardware and software,
Details of the work are published in the journal Scientific Reports.
The researchers from the UK universities of Lancaster and Manchester built tiny, layered metallic structures in the lab and incorporated "design flaws" that were unique to the item.
"What you do is shrink these systems down as far as they will go," co-author Jonathan Roberts from Lancaster told BBC News.
"And the interesting thing is that you can't clone them. To clone them, you'd effectively have to measure [the fingerprints] atom-by-atom. You just can't do it."
The fingerprint structures were demonstrated at the nano-scale where the laws of quantum mechanics take over from the ones that predominate at larger scales.
But the researchers say it is a proof of principle which could be integrated into existing chip manufacturing processes.
"These could be used to authenticate any electronic equipment and be 100% secure," said Mr Roberts.
"Having one of these devices in each and every piece of electronic equipment, you could challenge that electronic device and see what it outputs in order to identify it."
"If you imagine self-driving cars communicating with a fake server, that could have dramatic consequences."
The technology is already being commercialised through a spin-out company Quantum Base.
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World doubles number one Jamie Murray and partner Bruno Soares reached the Monte Carlo Masters final with a 6-2 6-4 win over Marcelo Melo and Ivan Dodig.
[NEXT_CONCEPT]
A 37-year-old man has been arrested on suspicion of murder after a woman who was found in her east London flat with serious injuries died.
[NEXT_CONCEPT]
An atomic-scale fingerprint could boost the security of connected devices, according to British scientists who have developed it.