Top-seeded Nadal pounded his way past Denis Istomin of Uzbekistan 6-2, 7-6, 7-5 in the featured night session match on Arthur Ashe Stadium court.
Fourth-seeded Murray saw off Jamaica’s Dustin Brown 7-5, 6-3, 6-0 on the same court earlier in the day.
Nadal next plays France’s Gilles Simon who defeated Philipp Kohlschreiber of Germany 4-6, 6-3, 1-6, 6-1, 6-3, while Murray takes on Stanislas Wawrinka of Switzerland who ousted Juan Ignacio Chela of Argentina 7-5, 6-3, 6-4.
There were mixed fortunes for US hopes with teenager Ryan Harrison squandering three match points against Ukraine’s Sergiy Stakhovsky in a fifth set tie-breaker before losing 6-3, 5-7, 3-6, 6-3, 7-6.
But Sam Querrey and John Isner both won through in the same quarter as Murray.
At the start of the day there were nine Spaniards and seven Frenchmen involved in the 16 ties that made up the top half of the draw.
By the end of play, seven of the Spanish had survived (the two losers going down to compatriots) and only two Frenchmen remained.
Nadal — seeking in New York to become just the seventh man to complete the career Grand Slam of Australian, French, Wimbledon and US crowns — was made to dig deep from 1-5 down in the second set tie-break against the 39th-ranked Istomin, taking six points in a row.
He then grabbed the only additional break he needed in the 12th game of the third set to clinch the win.
Murray had been expected to sweep past the unconventional Brown with little or no effort, and in the end he did so.
But he was left scratching his head at times in the first set by the towering Brown’s unorthodox play focused around a huge, whipping serve and some outrageous drop shots.
On top of that, early play was suspended for around 20 minutes as, courtesy of Hurricane Earl churning up the US eastern seaboard, a rain shower dampened the Flushing Meadows courts.
In the end, the dreadlock Brown, ranked 123rd in the world, had little left to offer and Murray even went for some extra practice afterwards to complete his day.
The emotional high of the day for home fans came out on the atmospheric Grandstand Court where 18-year-old Harrison, the youngest player left in the tournament, had three match points against Ukraine’s Stakhovsky in the fifth set tie-break.
But a double fault and some brave net play from a tiring Stakhovsky saved the day for the east European.
There was better news for US hopes, however, shortly afterwards on the adjacent Louis Armstrong Court when Wimbledon marathon man Isner won through to the third round with a 6-3, 3-6, 7-6, 6-4 win over Marco Chiudinelli of Switzerland, setting up a third round clash against Mikhail Youzhny of Russia.
Querrey then cruised past Spain’s Marcel Granollers 6-2, 6-3, 6-4.
Tommy Robredo got the Spanish challenge off to strong start when his French opponent, Julian Benneteau, retired in a second set tie-break after injuring his left wrist stretching for a shot. Robredo had won the first set 6-4.
David Ferrer, the 10th seed, then bulldozed his way past Benjamin Becker of Germany 6-3, 6-4, 6-4 and Feliciano Lopez saw off the challenge of France’s Benoit Paire 6-4, 6-7, 5-7, 7-6, 6-2.
French hopes suffered another blow when Jeremy Chardy fell to Daniel Gimeno-Traver of Spain 4-6, 6-2, 6-0, 7-6 and then Fernando Verdasco ousted Chardy’s compatriot Adrian Mannarino 6-1, 6-2, 6-2.
But serve and volley expert Michael Llodra brought some consolation for the French when he defied a painful left foot injury to defeat Victor Hanescu of Romania 7-6, 6-4, 6-2.
And late in day, Simon came through against Kohlschreiber to set up a third round clash with Nadal.