Tsonga, the French ninth seed, overcame Kazakh Aleksandr Nedovyesov 6-3 6-4 6-4 on a warm Thursday in New York.
The 2008 Australian Open runner-up hit 13 aces, but Nedovyesov was left to lament missed chances.
While Tsonga broke serve four times from eight chances, Nedovyesov could only capitalise on one of his opportunities despite creating as many as the 29-year-old.
Awaiting Tsonga in the third round is Pablo Carreno Busta after the Spaniard was too good for Frenchman Benoit Paire in a 6-1 6-4 3-6 6-3 victory.
Canadian fifth seed Raonic sent down 26 aces in a 7-6 (7-4) 5-7 6-4 7-6 (7-3) win over German Peter Gojowczyk.
Raonic, who has never been beyond the fourth round at Flushing Meadows, will face the Dominican Republic's Victor Estrella Burgos.
The 34-year-old beat 17-year-old Croatian Borna Coric 7-6 (7-2) 4-6 6-4 6-2.
Serbian world number one Djokovic claimed a routine 6-1 6-3 6-0 win over Frenchman Paul-Henri Mathieu.
Next up for Djokovic is big-serving American Sam Querrey, who brushed past Spanish 28th seed Guillermo Garcia-Lopez 6-3 6-4 6-4.
Andy Murray, the British eighth seed, also eased through as he beat German Matthias Bachinger 6-3 6-3 6-4.
The two-time grand slam champion will face Andrey Kuznetsov after the Russian's surprise 6-3 4-6 4-6 7-5 6-3 win over Spanish 31st seed Fernando Verdasco.
American 13th seed John Isner had no problems in a 7-6 (7-5) 6-4 6-2 win over German Jan-Lennard Struff.
Isner will face another German in Philipp Kohlschreiber after the 22nd seed claimed the first set 6-2 over Michael Llodra and the Frenchman retired.
Japanese 10th seed Kei Nishikori also benefitted from a retirement, leading Pablo Andujar 6-4 6-1 when the Spaniard called it quits.
Awaiting Nishikori is Argentine 23rd seed Leonardo Mayer, who eased past Australian Matthew Ebden 6-1 6-3 6-4.
Spanish 16th seed Tommy Robredo battled to a 5-7 6-7 (5-7) 6-4 6-3 6-2 win over Italian Simone Bolelli.
Robredo faces a tricky clash against Nick Kyrgios next after the Australian teenager comfortably beat Italian Andreas Seppi 6-4 7-6 (7-2) 6-4.