"It was a pretty good start, but I can do better, " Tsonga told the ATP Tour.
The No. 6 seed Jo-Wilfried Tsonga, from France, triumphed 7-6 6-2 over Russia's Nikolay Davydenko.
Wawrinka replaced Jo-Wilfried Tsonga in the field after the Frenchman pulled out with a wrist injury.
Next up is the unseeded Ukrainian Dolgopolov following his shock victory over 2008 runner-up Tsonga.
At the French Open, Djokovic saved four match points in the quarterfinals against Tsonga.
He stunned Tsonga with a display of attacking tennis and quickly took a one set lead.
He controlled matters from the outset against Tsonga on another searingly hot day in Montreal.
Spain's Feliciano Lopez will play third seed Jo-Wilfried Tsonga of France in the other semifinal Saturday.
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Jo-Wilfried Tsonga, seeded seventh, came from a set down to defeat Spain's Fernando Verdasco 4-6 6-3 6-2.
Elsewhere, French eighth seed Jo-Wilfried Tsonga suffered a shock defeat by Jerzy Janowicz, going down 6-4 7-6.
Tsonga also made the long trip, but exited in the first round to fellow Frenchman Michael Llodra.
It is not so easy for Tsonga or Soderling to reach the final and win the tournament.
Tsonga advanced when Michael Llodra retired from the all-French match after dropping the first set 7-6 (11-9).
Both players were battling illness, and Tsonga said he was close to withdrawing before Llodra pulled out.
Tsonga started strongly to break the favorite, but Djokovic retrieved it before winning the first set tiebreak.
It took 47th-ranked Chardy just 88 minutes to dispatch Tsonga, who could not convert on three break points.
His opponent Wednesday will be No. 9 Marin Cilic, who defeated No. 6 Jo-Wilfried Tsonga 7-5, 7-6 (4).
Tsonga looked to have restored confidence in the second set until Klizan restored his advantage in the third.
If Tsonga prevails the tie will hinge on the final match which sees Ryan Harrison play Gilles Simon.
Murray also made it through to the last four in London, beating Frenchman Jo-Wilfried Tsonga 6-2 7-6 (7-3).
Tsonga's win could hardly have been in greater contrast to Sunday's epic five-set first-round success against Daniel Brands.
Nadal will now meet Gilles Simon after he won his all French clash with Jo-Wilfried Tsonga 7-5 6-4.
French eighth seed Jo-Wilfried Tsonga came through a titanic battle with unfancied German Daniel Brands on Court Phillippe Chatrier.
Nadal will now face France's Jo-Wilfried Tsonga, who saw off Stanislas Wawrinka 2-6 6-3 6-4 in his quarterfinal tie.
Third seed Tsonga, an Olympic doubles silver medalist in London, was beaten 6-4 7-6 by fellow Frenchman Jeremy Chardy.
"It's an incredible challenge, " Tsonga told reporters of his upcoming contest with Nadal.
"Simply said it was that Tommy played better than me, " Tsonga told AFP.
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There were also wins for France's Jo-Wilfried Tsonga, Italy's Andreas Seppi, Belgium's David Goffin and eighth seed Richard Gasquet.
Once Djokovic took the fourth-set tiebreak, Tsonga folded quickly: 6-1 Djokovic it went.
Tsonga would get four match points in total, but Djokovic defended them all.
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