Djokovic - aiming to reach his fifth consecutive final at Flushing Meadows - disposed of the American 6-3 6-2 6-2 in their third-round clash on Saturday.
Breaking twice early on, the Serbian world number one found himself 5-0 to the good after just 15 minutes - losing only nine points in the process.
While Querrey recovered to win the next three games, it was not enough as Djokovic held firm to see out the opening set.
A first-serve percentage of 80 in the second set helped the 2011 US Open champion continue his dominance as the 27-year-old went 6-3 6-2 ahead in less than an hour.
Querrey - who made the semi-finals in Winston-Salem earlier in August - offered some resistance in the final set as he produced four aces.
However, Djokovic broke twice more before converting match point number two to set up a fourth-round showdown against German 22nd seed Philipp Kohlschreiber.
Kohlschreiber outlasted 13th-seeded American John Isner 7-6 (7-4) 4-6 7-6 (7-2) 7-6 (7-4).
It was the third successive year Kohlschreiber has knocked out Isner in the round-of-32 in New York.
Joining Djokovic in the fourth round was Tsonga after the Frenchman made light work of unseeded Spaniard Pablo Carreno Busta.
Tsonga - a quarter-finalist in New York in 2011 - had 14 aces and 32 winners as he won 6-4 6-4 6-4 to earn a meeting with eighth seed Andy Murray.
Murray had to dig deep in his first meeting with Russian Andrey Kuznetsov despite dominating the first set, before ultimately coming through 6-1 7-5 4-6 6-2 to seal his progress.
Swiss third seed Stan Wawrinka did not have to take his place out on Louis Armstrong Stadium after Blaz Kavcic withdrew.
The Slovenian cited a right foot injury as Wawrinka was handed a walkover through to the last-16, where he will face Spaniard Tommy Robredo.
Robredo - the 16th seed - came from a set down to end the tournament of Australian teenager Nick Kyrgios, winning 3-6 6-3 7-6 (7-4) 6-3.
Seeds Milos Raonic and Kei Nishikori will go head-to-head in the next round after both players recorded victories on Saturday.
Canadian fifth seed Raonic needed three tie-breaks to see off Dominican Republic's Victor Estrella Burgos 7-6 (7-5) 7-6 (7-5) 7-6 (7-3) in two hours and 43 minutes.
Japan's Nishikori - the 10th seed - had a much easier task, accounting for Argentine Leonardo Mayer 6-4 6-2 6-3.