The No. 31 seed recorded a straight-sets 6-2 6-2 6-4 win over Spain's Feliciano Lopez.
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Murray will meet Tomas Berdych in the fourth round on Sunday after the Czech Republic 15th seed enjoyed a straight-sets win over American John Isner, ranked 17.
Bucknell is the top seed for the third straight year and opens against last-place and eighth-seeded Navy.
Earlier Zheng's compatriot Li Na followed her into the quarterfinals after stunning fourth seed Caroline Wozniacki in straight sets.
Also on Wednesday, Caroline Wozniacki's terrible 2013 continued when the number one seed was beaten in straight sets by China's Zheng Jie at the Brussels Open.
But while destiny seems to be on her side at Flushing Meadows, Clijsters will be all too aware that world number eight Zvonareva - who earlier upset top seed Caroline Wozniacki in straight sets - has beaten her in their two most recent meetings.
Kuznetsova, meanwhile, will now play fellow Russian Kirilenko after the 30th seed beat Yvonne Meusburger in straight sets.
The top seed also beat Willstrop in straight sets to win the Commonwealth Games title in Delhi last October.
Last year's runner-up and second seed Dinara Safina was made to battle for her first win beating Magdalena Rybarikova 6-4 6-4 in 89 minutes, while fellow-Russian and third seed Svetlana Kuznetsova was a straight-sets winner over Anastasia Rodionova 6-1 6-2.
Latvia's Gulbis, seeded 24th, lost in straight sets to Jeremy Chardy , 28th seed Radek Stepanek lost 6-4 6-2 4-6 6-4 to Julien Benneteau and 30th seed Juan Monaco was sent packing by Canada's Peter Polansky in straight sets.
Fourth seed Venus followed up her opening win over Patty Schnyder with another routine straight-sets victory, defeating Israeli 16th seed Shahar Peer 6-3 6-4.
Second seed Nadal defeated Gael Monflis in straight sets, to book his place against compatriot Nicolas Almagro.
In the accompanying WTA event, top seed and World No.1 Victoria Azarenka swept past second seed Maria Sharapova of Russia in straight sets in the final.
Meanwhile, former champion and local favorite Philipp Kohlschreiber is out of the BMW Open in Munich after going out in straight sets to second seed Marin Cilic.
With much of the Bay Area crowd still basking in the earlier win by California, Syracuse got off to a fast start to put to rest any questions about whether a third straight double-digit seed team would win in San Jose following wins by the Bears and Oregon earlier in the day.
The Rangers can probably forget about earning the top seed in the conference for the second straight season.
Cilic was joined in round three by French fifth seed Jo-Wilfried Tsonga and Spanish sixth seed Fernando Verdasco, who both recorded straight-sets victories.
Henin is also on the comeback trail, inspired by Clijsters' exploits, and returned with a superb straight sets win over second seed Nadia Petrova on Monday.
It is the third year running that Federer has beaten Djokovic in New York and the top seed is closing in on a sixth straight US Open title.
But 19th seed Mardy Fish , runner-up to Roger Federer in Cincinnati , recovered from a mid-match wobble to overcome Jan Hajek 6-0 3-6 4-6 6-0 6-1 and 23rd seed Feliciano Lopez beat Santiago Giraldo in straight sets.
Home hopes were boosted by an easy straight sets win for seventh seed Andy Roddick over Thiemo de Bakker of the Netherlands while in-form Jo-Wilfried Tsonga of France was taken to three sets before beating Albert Montanes of Spain, 4-6 6-3 6-3.
The Russian fourth seed's last match was a humiliating straight sets loss to veteran Italian Davide Sanguinetti at the Miami Masters in March.
Sixth seed Juan Martin del Potro eased past German Benjamin Becker 6-2 6-4 6-2, while French seventh seed Jo-Wilfried Tsonga battled to a straight-sets win over Japan's Go Soeda.
Eleventh seed Gonzalez of Chile and number three seed Nadal of Spain were in their 2nd straight tie-breaking set, with Nadal leading 7-6 (7-4), 6-6 (3-2) when play was suspended.
The third seed made light work of Japan's Ayumi Morita 6-1 6-3 to set up a fourth round tie against 14th seed Maria Kirilenko from Russia who was also a straight sets winner (7-6 6-3) over Belgium's Yanina Wickmayer.
The 25-year-old Djokovic will play Ukrainian 14th seed Alexander Dolgopolov, who dispatched Stanislas Wawrinka of Switzerland in straight sets.
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