Soderling will take on third-seeded Novak Djokovic, who defeated French qualifier Arnaud Clement 6-2, 6-2.
Soderling needs to at least reach the final to have a chance of qualifying for the season-ending event in London this month.
The sixth-seeded Davydenko, who won in Paris in 2006, could have secured one of the two spots still up for grabs with a win but can still qualify depending on his rivals' results.
Soderling, who reached his second quarterfinal in Paris, broke Davydenko in the fourth game of the first set. Davydenko called for the trainer while trailing 5-2 and was given a pill but was unable to prevent his Swedish opponent from closing out the set with a service winner on his first set point.
Davydenko broke Soderling to love with a backhand return winner down the line to lead 2-0. The 28-year-old Russian then saved a break point with a forehand volley at 30-40 in the seventh game and leveled with a cross-court backhand volley that Soderling was unable to chase down.
At 5-4 to Soderling in the decider, Davydenko threw his racket in anger after sending a backhand wide that gave his opponent two match points. The 25-year-old Swede converted the first one when Davydenko missed another backhand.
Davydenko and Soderling are among five players still in the running to secure the two remaining spots in the ATP World Tour Finals. The others are Jo-Wilfried Tsonga, Fernando Verdasco and Fernando Gonzalez.
Djokovic, coming off a win over top-ranked Roger Federer in the Swiss Indoors final last week, reached the quarterfinals for the first time after winning 80 percent of the points played on his first serve. Clement saved two match points before Djokovic took the match when his opponent put a forehand into the net.
Second-seeded Rafael Nadal, who saved five match points to reach the third round, will later face 14th-seeded Tommy Robredo, while defending champion Tsonga plays Gilles Simon.