Davydenko and Tsonga are among five players who can still qualify for the eight-man, season-ending event in London. Fernando Verdasco, Robin Soderling and Fernando Gonzalez are also in the running to secure the two remaining spots.
The 28-year-old Davydenko, who won the Paris Masters in 2006, needs to reach the semifinals to take a spot, while Tsonga must defend his title without facing Verdasco in the final to advance.
Tsonga showed no signs of the wrist injury that forced him to retire in the first round of the Valencia Open last week. The eighth-seeded Frenchman won five straight games in the first set. He broke in the 11th game of the second and closed it out on his first match point.
Davydenko, who broke Becker five times and saved four break points, said he didn't feel under pressure going into this week.
"There are three guys who need to win this tournament to qualify," said Davydenko, who has won four titles this season. "It won't be easy for the likes of Tsonga, Soderling or Verdasco and it makes me feel good."
The seventh-seeded Verdasco rallied to beat Andreas Seppi 6-7 (3), 6-4, 6-4. The 25-year-old Spaniard closed out the match on his first match point with a service winner and eliminated two contenders from the race to the ATP World Tour Finals -- Radek Stepanek and Marin Cilic.
Verdasco, who had his foot bandaged in the third set, broke Seppi in the ninth game of the decider and served out the match.
Verdasco will play in London later this month if he wins in Paris but could qualify earlier depending on his rivals' results.
"It was my big challenge for this year, and this week is the last week," Verdasco said. "After this, everything is going to be decided. So I'm giving my best in the last chance, the last week to try to do it."
Verdasco will face either 12th-seeded Marin Cilic or qualifier Lukasz Kubot.
Davydenko won 71 percent of points on serve and had five aces against Becker. His next opponent will either be Soderling or Ivo Karlovic.
"This tournament is always difficult, and this kind of surface is the most difficult of the year for me," said Nadal, who has never won the Paris Masters. "And I think it's faster than the other years. The bounce is lower, but that's it."
French qualifier David Guez, 179th in the rankings, defeated Stanislas Wawrinka 6-3, 6-4 to reach the second round. Juan Monaco of Argentina broke Jeremy Chardy of France three times on his way to a 7-6 (6), 7-5 victory.