Swiss third seed Wawrinka, the Australian Open champion, was expected to be challenged by talented Czech Jiri Vesely but completed a relatively comfortable 6-2 7-6 (8-6) 7-6 (7-3) win.
Wawrinka produced 41 winners in the first-round clash at Flushing Meadows, where he was a semi-finalist last year.
Tsonga, another potential challenger to Djokovic and Roger Federer for the title, overcame Argentine Juan Monaco 6-3 4-6 7-6 (7-2) 6-1.
The French ninth seed sent down 20 aces and 48 winners in a powerful display against a tricky opponent.
Despite his scratchy form, Serbian world number one Djokovic was never likely to be troubled by Argentine Diego Sebastian Schwartzman and that proved to be the case as he won 6-1 6-2 6-4.
Briton Murray battled cramps in the New York heat before the eighth seed eventually got past Dutchman Robin Haase 6-3 7-6 (8-6) 1-6 7-5.
It came on a good day for the seeds in New York.
Only Mikhail Youzhny (21st seed) and Julien Benneteau (24th) failed to advance to the second round.
Russian Youzhny was beaten 7-5 7-6 (7-4) 2-6 7-6 (7-1) by fiery Australian teenager Nick Kyrgios.
Benoit Paire edged his French countryman Benneteau 7-6 (7-4) 5-7 6-4 4-6 6-4 in four hours four minutes.
Canadian fifth seed Milos Raonic sent down 20 aces in a comfortable 6-3 6-2 7-6 (7-1) win over Japan's Taro Daniel.
Veteran Spaniard Tommy Robredo (16th seed) brushed past France's Edouard Roger-Vasselin 6-4 6-3 6-4 and German Philipp Kohlschreiber (22nd) was a convincing 6-2 7-6 (7-3) 6-3 victor over Argentine Facundo Bagnis.
There was better luck for another Argentine, Leonardo Mayer, with the 23rd seed leading Albert Montanes 6-2 3-0 when the Spaniard retired with a wrist injury.
French 30th seed Jeremy Chardy was made to fight to get past left-handed Colombian Alejandro Falla 6-7 (5-7) 6-2 7-5 6-4.
Fernando Verdasco, the Spanish 31st seed, battled to a 6-3 3-6 7-5 1-6 6-4 win over Slovenian Blaz Rola.
Slovenian Blaz Kavcic and Italian Simone Bolelli were surprisingly comfortable winners.
Kavcic beat American Donald Young 7-5 6-4 6-4 and Bolelli completed a 2-6 6-4 6-2 3-6 6-3 win against Canadian Vasek Pospisil.
Frenchman Michael Llodra eased past Spaniard Daniel Gimeno-Traver 6-4 6-3 7-5, Russia's Andrey Kuznetsov beat American Bradley Klahn 6-4 4-6 6-3 7-5 and Kazakh Aleksandr Nedovyesov was a 4-6 6-2 6-1 7-6 (7-3) winner over Irishman James McGee.
German Matthias Bachinger upset Czech Radek Stepanek 6-3 6-2 6-2, Italian Andreas Seppi cruised past Ukrainian Sergiy Stakhovsky 6-3 6-1 6-4 and Australian Matthew Ebden crushed Tobias Kamke 6-4 6-3 7-6 (7-2).
France's Paul-Henri Mathieu needed over four hours to beat Luxembourg's Gilles Muller 6-7 (7-9) 7-5 7-6 (8-6) 6-7 (5-7) 6-1 and Peter Gojowczyk thrashed Benjamin Becker 6-2 6-4 6-2 in their all-German affair.
Brazilian Thomaz Bellucci was a 7-6 (7-4) 6-4 6-1 winner against France's Nicolas Mahut and Spain's Pablo Carreno Busta beat German Andreas Beck 6-3 4-6 6-2 7-6 (7-0).