Murray proved physically and mentally stronger than the Frenchman as he weathered an early storm before holding out for the win.
Murray will move up to number two in the world, overtaking Roger Federer, if he wins the title on Sunday. Standing in his way is the tenacious David Ferrer to do that, the Spaniard ending the run of Tommy Haas earlier in the day to book his final berth.
Gasquet made a scintillating start to the match, breaking in just the second game by rattling a spectacular backhand passing shot down the line.
A second love service game quickly followed from the Frenchman and Murray, champion in Miami in 2009 and a beaten finalist last year, looked more than just a step too slow, but actually rattled.
The early deficit make Murray adapt a much more aggressive tactic, a move that paid dividends almost immediately.
The world number three broke back in the fifth game of the set, a flicked forehand winner down the line bringing up the break points before Gasquet conceded with a poor serve. The Scot then broke again, this time for the lead, in the ninth game when Gasquet failed to find the court with a forehand.
But, just when it looked like Murray might be hitting cruise control in the match, a poor game from him allowed Gasquet to break back immediately and the opening set headed into a tie-break.
A poor breaker from Murray, combined with some sparkling play from Gasquet, allowed the Frenchman race through and take the first set 7-3 in the breaker after Murray pulled a cross court backhand wide.
The early exchanges in the second set suggested there would be little to separate the players, neither appearing to have the edge in terms of momentum.
But Murray suddenly found another gear, breaking in both the fourth and sixth games (the latter with an exquisite backhand lob right onto the baseline) as he levelled the match in double-quick time.
Gasquet had an injury timeout for attention to blisters on the sole of his right foot in between the second and third sets, and looked completely beaten when Murray broke in the opening game of the decider.
Murray let the Frenchman back into the match again, however, immediately conceding his serve by opening and closing the second game with a double fault.
Gasquet was running out of energy, though, and Murray re-established his break advantage in the third game, when his opponent slipped on the baseline and netted a forehand to cede his serve once again.
This time Murray refused to make the same mistake, holding to consolidate the break before taking the Frenchman's serve again in the seventh game and serving out the match at the first attempt.