Defending champion Davydenko, the top seed, struggled to keep pace with Argentina's Juan Monaco and slumped to a 6-2, 6-7, 6-4 defeat at the Poertschach International.
The world No 1 was taken the distance by Argentine qualifier Juan Monaco at the Hamburg Masters.
Ivo Karlovic ousted sixth seeded German Benjamin Becker 7-5 7-6 in the first round of the U.S. Clay Court Championships on Monday.
Top seed Carlos Moya recorded another straight-sets win at the $380,000 Buenos Aires Open on Wednesday.
Carlos Moya enjoyed a straight-sets win over qualifier Peter Luczak in the first round of the $380,000 Buenos Aires Open.
Fourth seed Andy Murray erased memories of early losses at Indian Wells by storming into the BNP Paribas Open third round with a ruthless 6-1, 6-3 victory over Canadian Vasek Pospisil on Saturday.
Britain's Andy Murray enjoyed a routine win over Argentina's Juan Monaco to ease into the third round of the tennis tournament at the Rio Games on Tuesday, while Spain's world number nine David Ferrer was knocked out.
Second seed Gael Monfils edged past Croatia's Ivo Karlovic 7-6(6), 7-6(6) and Marin Cilic ousted Argentine Juan Monaco 7-5, 6-1 to progress to the Japan Open semi-finals in Tokyo on Friday.
Rafael Nadal won his first title of the year with a 6-4, 6-1 victory.
Rafael Nadal, working his way back to top form after wrist problems last year, screamed with delight on reaching the Argentine Open semi-finals with a 6-1 6-1 rout of Federico Delbonis on Friday.
According to Hola magazine, Nadal and Xisca got secretly engaged in May last year and now planning an autumn wedding this year.
India's Rohan Bopanna and his Pakistani partner Aisam Qureshi crashed out of the US Open after going down fighting in the men's doubles first round contest at the Flushing Meadows in New York.
Seventh seed Wawrinka of Switzerland set up a third-round meeting with Bulgarian ninth seed Grigor Dimitrov after seeing off Argentine Juan Monaco 6-4, 6-1.
Olympic tennis champion Andy Murray said he is playing the best tennis of his career at the moment and is confident of clinching his second US Open title, starting later this month.
A summary of sports events and sports persons, who made news on Tuesday
Olympic and Wimbledon champion Andy Murray picked up where he left off in Rio by drubbing Argentina's Juan Monaco to take his place in the third round of the Western & Southern Open in Cincinnati on Wednesday.
Novak Djokovic scraped over his first hurdle at the Rome Masters.
Defending champion Novak Djokovic survived a scare.
Olympic champion and world number one Serena Williams tumbled out of the Rio de Janeiro singles competition in the third round on Tuesday after a shock defeat to Ukraine's Elina Svitolina.
Rafael Nadal made up for his semi-final defeat at the Rio Open a week ago by reaching the Argentine Open final with a 7-6, 6-2 victory over Carlos Berlocq.
US Open champion Marin Cilic made a shock first-round exit from the Shanghai Masters on Monday after losing 7-5, 2-6, 7-6(2) to fellow Croatian Ivo Karlovic.
Serbia's Novak Djokovic is the top seed in the men's draw which includes five-times US Open champion and 17-times Grand Slam winner Roger Federer as seventh seed - his first time the Swiss has been placed outside the top three in a Grand Slam in over ten years.
World No 1 Novak Djokovic and fourth-seeded Andy Murray each had to contend with different degrees of adversity before they advanced.
The winners of the season's first three grand slams Novak Djokovic, Andy Murray and Rafa Nadal put on a masterclass at the Western and Southern Open on Wednesday, strolling into the third round with straight sets wins.
The Argentine, making his first appearance at Wimbledon since reaching the semi-finals in 2013, held aloft his arms in triumph after condemning twice Grand Slam champion Stan Wawrinka to his earliest defeat at the All England Club for three years.
Soccer's governing body FIFA has agreed to ban the third-party ownership (TPO) of players, its president Sepp Blatter said on Friday, seven years after first promising to outlaw the practice.