The world number three allowed the French 10th seed to come back into the contest when he was let down by his first serve in the second set, but regained his momentum to book a meeting with David Ferrer.
With the two big events coming up later this month, Murray was hoping to be challenged and he was not disappointed.
"You don't want to play loads of those matches over the next few weeks, but I played two extremely quick matches the first two rounds," the second seed told a news conference.
"So to get a long one, for me, and I think in that atmosphere as well, with the Davis Cup coming up is a very positive thing for me, you know, to go through that physically and emotionally."
Murray got off to a strong start, breaking in the second game on his way to a 3-0 lead.
Gasquet, however, remained aggressive, took his chances and was rewarded with a break of serve in the seventh game as his opponent grew cautious.
Gasquet, backed by the partisan Bercy crowd, went 5-3 up in the tiebreak and at 6-5 Murray saved a set point with a superb sliced passing shot.
The Scot then won four of the five remaining points to clinch the first set.
Murray was forced onto the back foot in the second and managed only six winners compared to 20 in the opening set as Gasquet easily levelled the match.
The Olympic and twice grand slam champion struggled on serve and allowed his opponent to break for 2-1 in the decider but quickly got back on track.
He stole Gasquet's serve before breaking decisively for 5-3 and wrapped it up on serve to secure his first semi-final appearance at the Paris Masters.
The World Tour finals will be played at the O2 in London from Nov. 15-22 and Britain will face Belgium in Ghent for the Davis Cup final from Nov. 27-29.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
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