Gil was making history as the first Portuguese man to make the third round of a grand slam, but he never looked like going any further with Tsonga displaying too much power and guile to complete a routine 6-2 6-2 6-2 victory in just 91 minutes.
"Today I played well and felt good on court," Tsonga said. "Match after match I play better here and I hope it will continue and I go far in the tournament."
Andy Murray came through unscathed against Michael Llodra, winning 6-4 6-2 6-0 to continue his quest for a third successive Australian Open final.
The Frenchman tried to throw Murray off course with his net-rushing style but it simply gave the world number four a target which he frequently beat with some wonderful passing shots.
Llodra tried everything to get back into the contest with numerous through the legs shots but Murray was not to be denied as he cruised through 6-4 6-2 6-0.
Next up for the Scot is Mikhail Kukushkin, who prevailed in an extraordinary match against Gael Monfils. At a set and two breaks down, Monfils looked as though he was going to quit due to a lower back injury sustained early on. But he battled on and after dropping the second set hit back to take it to a decider.
It reached 5-6 30-15 with Monfils serving when a point was disrupted by a spectator throwing a ball on to the court in what turned out to be a pivotal moment as the 14th seed's concentration deserted him, coughing up two double faults including one on match point.
Richard Gasquet powered into the last 16 with a straight-sets defeat of ninth seed Janko Tipsarevic.
The Frenchman was at his stylish best to see off the Serbian 6-3 6-3 6-1.
Gasquet cruised through the first two sets, breaking once in the opener and twice in the second as an out-of-sorts Tipsarevic struggled to make an impression.
He finally claimed a break of his own deep in the third set, but Gasquet hit straight back to snuff out the danger and complete an impressive victory.
The 17th seed will play David Ferrer next following the Spaniard's 7-5 6-2 6-1 victory over veteran Argentinian Juan Ignacio Chela.
Defending champion and world number one Novak Djokovic motored through into the fourth round with a 6-0 6-1 6-1 thumping of Frenchman Nicolas Mahut.
Japanese hope Kei Nishikori continued his good form with a 4-6 7-6 7-6 6-3 win over Julien Benneteau.
Day 6 Australian Open Men's Results
Jo Wilfried Tsonga def Frederico Gil 6-2 6-2 6-2
Mikhail Kukushkin def Gael Monfils 6-2 7-5 5-7 1-6 6-4
Richard Gasquet def Janko Tipsarevic 6-3 6-3 6-1
David Ferrer def Juan Ignacio Chela 7-5 6-2 6-1
Kei Nishikori def Julien Benneteau 4-6 7-6 7-6 6-3