Both players held serve early in the match, trading blows at 2-2.
Gasquet then held again before going 40-0 after a five-shot rally on Russell's serve. The Frenchman subsequently broke his opponent to take a 4-2 lead midway through the first set.
He appeared to be on course to win the first set with a 40-0 lead on his serve, but Russell fought back to deuce. However, Gasquet maintained his composure to win the opening set 6-3.
A lengthy opening game of the second ensued before Russell held. Gasquet broke his opponent again at 2-1, before winning a six-shot rally to edge further ahead.
Russell, playing in front of his home crowd, felt further disappointment soon after as Gasquet broke for the second time in the set at 4-1.
Russell managed to claw back into the set however, breaking his opponent's serve and holding his own to narrow the deficit to 4-3.
Both players then held their service games, leaving Gasquet to serve out the second set 6-4.
The third set was far more comfortable for Gasquet after breaking in the first game.
He then held serve to complete the win.