Eighth seed Gasquet started like a train before claiming the first set on a tie-break, but Murray asserted his authority in the second and third sets of an entertaining semi-final.
Murray will next take on third seed Ferrer, who beat veteran German Tommy Haas in the opening semi, with the Briton playing both for the title and the number two spot in the world rankings. A win will take him above Roger Federer.
"The first set was a tough one to lose," Murray told Sky Sports 2. "I hit something like 20-odd winners, so to lose it was tough.
"I felt like I was dictating a lot of the points but just made a few unforced errors on the backhand side at the end.
"I did well in the second and third sets to keep up my intensity."
Gasquet manoeuvred Murray around the court to create a break point opportunity in the Briton's first game, then produced a stunning backhand pass to convert.
Two more flashing backhand winners helped the Frenchman take the next game to love, meaning he was yet to drop a point on serve at 3-0.
Murray held confidently to get on the board and finally took a point on the Gasquet serve via a double fault.
All of a sudden it was Murray bossing proceedings and he twice passed Gasquet as he brought up three break points then converted at the first time of asking and held to level at 3-3.
With Murray creating some outrageous angles on the forehand, he broke again for 5-4, but then threw the advantage away as he served for the set with an unforced error and a double fault, and the set went to a tie-break.
Gasquet took the advantage with an early mini-break and a stunning half-volley winner helped him bring up three set points, only one of which he needed.
The standard noticeably dipped at the start of the second, but some eye-catching defence from Murray, as he hammered a Gasquet overhead straight back at him, helped the Scot to break for 3-1.
That proved to be the turning point in the match.
A pinpoint lob helped Murray to another break for 5-1, then he held to love, sealing the set with an ace.
Gasquet received treatment to his feet at the end of the set, but it did nothing to switch the momentum as Murray broke again at the start of the third.
Murray contrived to bring his opponent back into the match as two double faults saw him surrender the advantage, but broke again immediately and this time it was decisive.
"He always comes up with unbelievable points," Murray said of Gasquet. "He's incredibly talented. In the tie-break he played two- pick-ups off his toes for clean winners. He's in the top 10 in the world and he's playing very well."
On the final against Ferrer, he added: "It will be a tough match.
"He's had a great week, he's in great shape. He's always tough to play against."
Ferrer needed to dig deep to end the resilience of Haas and reach the final.
Haas, who dumped out world number one Novak Djokovic earlier this week, looked set to claim another famous scalp when he took the first set.
But Ferrer came storming back to level matters and although the Spaniard trailed 3-1 in the decider, he showed his typical resolve to seal a 4-6 6-2 6-3 triumph.
The loss was tough on Haas, who came flying out of the traps, winning four games in a row to open up a 5-2 lead.
Ferrer lived up to his reputation of fighting for every point and clawed one of the breaks back but Haas held his nerve at the second opportunity.
The world number five had clearly taken some heart from his belated fightback and was formidable on serve in the second set.
He did not concede a single break point - winning 91 per cent of points on his first serve - and took his opportunities when returning.
He broke the world number 18 in the sixth game and then again in the eighth to level proceedings.
There were three breaks of serve at the start of the deciding set, with Haas taking a 2-1 lead before holding his serve comfortably.
But the never-say-die Ferrer stormed back to take the next four games before sealing victory after a little over two hours on his first match point.