Tsonga had 25 aces and kept the French Open champion off-balance with his powerful baseline game and inspired net play.
Nadal, who made several uncharacteristic errors in the match, will rest before he begins the defense of his Wimbledon title. The 25-year-old Spaniard won his sixth French Open title on Sunday and acknowledged that an early loss at Queen's may help his preparations for the third Grand Slam event of the year.
"Probably after losing the second set, mentally I lost my concentration," Nadal said. "The negative thing is I lost. The positive thing is I have few days off and can stop a little bit mentally. I can be a little bit more relaxed, because every day I play with pressure."
Nadal and Tsonga played just two points before rain interrupted the match. With the court covered, Nadal remained on his chair for several minutes to sign autographs before returning to the locker room.
The Spaniard fought off a break point in the sixth game of the first set, failed to convert three break points at 5-5 but claimed the last five points of the tiebreak.
After an exchange of breaks to start the second, Tsonga broke again to lead 5-4 and served out the set.
In the third, Nadal missed a critical forehand volley at the net on game point and the fifth-seeded Frenchman went on to break for 1-0. An inspired Tsonga dominated the rest of the match.
Roddick broke to a lead 2-1 and earned anther break in the fifth game with a forehand pass.
The American dominated the Spaniard in the second set, breaking again for 2-1 and holding for 3-1 before rain interrupted play. After a 1-hour, 45-minute delay, Roddick immediately broke again by forcing Verdasco to net a backhand volley.
Roddick failed to take advantage of two match points on Verdasco's serve. But he ended the contest in the next game with a second-serve ace on his fourth match point.
"My first rain delay of the year is out of the way," Roddick said.
Querrey's defeat came after his third-round match was suspended overnight at one set all. When play resumed, Ward earned the only break of the third set to lead 4-3. He fought off a break point as he served out the match.
"It's been unbelievable, last two matches," said Ward, who also defeated fourth-seeded Stanislas Wawrinka. "Best two wins of my career so far."