Murray recovered after making a mess of the first set where he was serving for it at 5-4 but double-faulted on break point and ended up losing out in the tie-break.
Gasquet had been playing some inspired tennis but he was outplayed in the second set and the Scotsman never looked in danger in the third.
"The first set was a tough one to lose, because I obviously served for the set and then at the end of the set you kind of look up at the stats and I had hit over 20 winners and lost the set," the Scotsman told reporters.
"So I realised I had to cut out the unforced errors. I did a good job of that. Halfway through the second set I started to find the right way to play, the right shots to go for and I did well after that," he said.
Gasquet had to receive treatment for a blisters and an ankle problem but refused to blame his ailments for his defeat.
"I didn't lose because of that. I lost because he was better," said the Frenchman.
"He serves well. He returns very good. He runs a lot. He defends. He's the best defender in the world and he never misses. He's a very good player."
A victory over Ferrer in the final would move Murray above Roger Federer into second place in the world rankings.
Ferrer ended German Tommy Haas's dream of reaching the Sony Open final with a 4-6 6-2 6-3 victory in Friday's semi-final.
The 34-year-old Haas, whose career looked close to finished after a series of injuries, beat world number one Novak Djokovic on his way to the last four and threatened another upset at Key Biscayne.
After the German clinched the first set, Ferrer turned things around in the second but trailed 3-1 in the third with Haas sensing a real chance of his first Masters Series final in 11 years.
But Ferrer fought back, taking advantage of some unforced errors from the fading German to secure the victory and his first place in a final at Miami.
Ferrer is bidding to lift his second Masters 1000 victory, having triumphed over Jerzy Janowicz in Paris last November.
The Spaniard was a beaten semi-finalist in Miami in 2005 and 2006.
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