Del Potro had 27 winners and only eight unforced errors in a 6-3, 6-3 win over Spain's Nicolas Almagro, while Tsonga dispatched Germany's Florian Mayer 6-2, 6-3.
Del Potro, the 2009 U.S. Open champion, has been steadily working his way back up the rankings after a wrist injury ruined his 2010 season.
The Argentine moved back into the top five for the first time in more than three years on Monday, and he believes he's capable of challenging Rafael Nadal, Novak Djokovic and Andy Murray for Grand Slam titles again.
A win in Shanghai would make a statement: He's never won a Masters title and he may need to get through both Nadal and Djokovic to do so.
"I felt close to them in some parts of the year, some matches during this year, like in Wimbledon (where he lost in the semifinals to Djokovic), or when I beat Djokovic (and) Murray in Indian Wells," he said.
"I'm doing well at the moment. Could be fantastic for me if I finish the year top five, top six, playing the (ATP Finals) in London."
The Argentine can clinch a berth in the year-end championships by making the Shanghai final.
Tsonga is also on the comeback trail. The flashy Frenchman missed several months with a knee injury and also parted ways with his coach, Roger Rasheed, after less than a year. He's slipped to No. 9 in the rankings — his lowest position in two years.
"I missed the game and it was tough to see my friends play," Tsonga said about his injury layoff. "But anyway, you know, sometime it's good because it makes your mind clear, so after that you come back sometimes stronger. That's what I will try to do."
Tsonga moved into the eighth and final qualifying spot for the ATP Finals with his win on Friday, just ahead of compatriot Richard Gasquet.
His semifinal opponent could be Djokovic — a player he's had trouble with in recent years. Tsonga won five of their first seven matches but the Serb has taken the last eight.
Djokovic, the defending champion, plays Frenchman Gael Monfils in the quarterfinals later Friday, while Nadal goes up against Switzerland's Stanislas Wawrinka.
Djokovic and Nadal have a combined 18-0 record against the pair.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)