Ahead of the last-eight encounter, Cilic had not lost to Tsonga since 2011, but in a fiercely-contested first set, it appeared as though he wouldn't have it all his own way against the 2008 Australian Open finalist.
However, in the ninth game of the set, the Croatian finally converted a break point on his opponent's serve to edge into the lead.
Tsonga had competed well during the first 45 minutes of the match, but he was second-best in the second as he won just three points on Cilic's serve, and the ninth seed comfortably breezed into a two-set advantage.
Before the third, a timeout was called as Tsonga had strapping applied to his knee, but the Frenchman, perhaps throwing caution to the wind, produced his best tennis of the match to extend the contest into a fourth set.
Tsonga had the momentum, but Cilic was able to withstand the offence that was coming from the other side of the court, yet after creating two match points on the Tsonga serve at 4-5, he was unable to take advantage.
Cilic missed another match point at 5-6, and he was made to pay as Tsonga stormed through the resulting tie-break to ensure that the contest went the distance.
The deciding set proved almost as hard fought as its predecessor, but Cilic landed a break to move 4-2 ahead and went on to open up two further match points, only to be thwarted by a tenacious Tsonga on both occasions.
After clawing his way back to deuce with the score at 5-4, Cilic wrong-footed Tsonga to establish a sixth match point, which he eventually converted when his forehand saw the Frenchman throw his return long.